Previous Year Questions: Surface Area & Volumes - 1

# Class 10 Maths Chapter 12 Previous Year Questions - Surface Area and Volumes

## 2023

Q1: The curved surface area of a cone having height 24cm and radius 7 cm, is
(a) 528 cm2
(b) 1056 cm2
(c) 550 cm2
(d) 500 cm      [2023, 1 Mark]
Ans:
(c)
We have, the height of cone. h = 24 cm and radius, r = 7 cm.We know that,
=
= 25
Now. curved surface area = πrl
= 22/7 x 7 x 25
= 550 cm2
Q2: Curved surface area of a cylinder of height 5 cm is 94.2 cm2. Radius of the cylinder is (Take π = 3.14
(a) 2cm
(b) 3cm
(c) 2.9cm
(d) 6cm      [2023, 1 Mark]
Ans:
(b)
Curved surface area of cylinder = 2πrh
⇒ 94.2 = 2 x 3 .14 x r x 5

⇒ r = 3 cm

Q3: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of five cylinder is 10 cm and its base is of radius 3.5 cm.

find the total surface area of the article.      [2023, 4/5/6 Marks]
Ans:
Radius of the cylinder (r) = 3.5 cm
Height of the cylinder (h) = 10 cm
Curved surface area = 2πrh
=
= 220 cm2
Curved surface area of a hemisphere = 2πr2
∴ Curved surface area of both hemispheres
=
= 154 cm2
Total surface area of the Article
= (220 + 154) cm2
= 374 cm2.

Q4: A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find total height of the room if it contains      [2023, 3 Marks]
Ans: Let r be the radius and h be the height of the cylindrical part and R be the radius of hemispherical part.

Now, volume of air =

⇒ h = 4
Now, radius of hemispherical part R = 1/2h = 2m
∴ Total height of the room = R + h = 2 + 4 = 6m

Q5: An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is (1/6)th of the volume of the cone is unfilled but hemisphere is formed on the top. Find volume of the ice-cream. Take (π = 3.14)     [2023, 3 Marks]
Ans: Radius of cone, r = 3 cm
Height of cone, h = 12 cm
Let x be the volume of unfilled part of cone.
Now, volume of cone, =
Volume of filled part of cone = Volume of cone - Volume of unfilled part of cone

Now, volume of ice-cream = volume of filled part of cone + volume of hemisphere
=
= 150.72 cm3

## 2022

Q1: The radios of the base and the height of a solid right circular cylinder are in the ratio 2:3 and its volume is 1617 cm3. Find the total surface area of the cylinder. Take [π = 22/7]  [2022, 3 Marks]
Ans:
Given ratio of radium and height of the right circular cylinder = 2:3
Let radius (r) of the base be 2x and height(h) be 3x.
Volume of cylinder, V = πr2h

Total surface area of cylinder = 2πr (h + r)

= 770 cm2

Q2: Case Study : John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items they decided the following dimensions:
Cap : Conical shape with base circumference 44 cm and height 24 cm.
Cake : Cylindrical shape with diameter 24 cm and height 14 cm.

Based on the above information answer the following questions.
(a) How many square cm paper would be used to make 4 such caps?
(b) The bakery shop sells cakes by weight (0.5 kg, 1 kg, 1.5 kg. etc..}. To have the required dimensions how much cake should they order if 650 cm3 equals 100 g of cake?
[2022, 4/5/6 Marks]
Ans: Paper required to make four caps is 2,200 sq.cm.
Weight of the cake for required dimensions is 1kg.
Step-by-step explanation:
(a) Given the base circumference of the cone, c = 44 cm
Height of a cone, h = 24 cm.
Base circumference of the cone, c = 2πr = 44 cm
Thus, the radius of the cone is

The curved surface area of the cone is given by

Substituting the values of h and r,

Thus, to make one cap, 550 sq.cm of paper is required.
Then to make four caps, the required paper is
500 x 4 = 2000 sq. cm
Therefore, 2,200 sq.cm of paper is required to make four caps.
(b) Given the diameter of cylindrical shape cake, d = 24 cm
Height of cylindrical shape cake, h = 14 cm.
Radius of the cylindrical shape cake,

Volume of the cylinder is given byV = πr2h
Substituting the values of h and r,

The required volume of the cylindrical shape cake is 6,336 cu.cm.
Given 650 cu.cm equals 100 g of cake.
Then the required weight of the cake is

Given the bakery shop sells cakes by weight of 0.5 kg, 1 kg, 1.5 kg, etc.
Since, ,therefore, the cake of 1kg should be ordered for required dimensions.

Q3: Three cubes of side 6 cm each, are joined as shown in given figure. Find the total surface area of the resulting cuboid.   [2022, 3 Marks]

Ans: The dimension of the cuboids so formed are
length = 18 cm
breath = 6 cm and height = 6 cm.
Surface area of cuboids = 2 (l× b + b × h + l × h)
= 2 × (18 × 6 + 6 × 6+ 18 × 6)
= 504 cm2

Q4: Case Study : A 'circus' is a company of performers who put on shows of acrobats, downs etc to entertain people started around 250 years back, in open fields, now generally performed in tents. One such 'Circus Tent is shown below.The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then
find
(i) the area of the canvas used in making the tent.
(ii) the cost of the canvas bought for the tent at the rate Rs. 200 per sq. m. if 30 sq. m canvas  was wasted during stitching.    [2022, 4/5/6 Marks]
Ans: According to given information, we have the following figure.

Clearly, the radius of conical part = radius of cylindrical part = 30/2 = 15 m = r  ...(say)
Let h and H be the height of conical and cylindrical part respectively.
Then h = 8 m and H = 9 m

= 17 m

(i) The area of the canvas used in making the tent
= Curved surface area of cone + Curved surface area of cylinder
= πrl + 2πrH
= πr(l + 2H)

= 1650 m2
(ii) Area of canvas bought for the tent
= (1650 + 30) m2
= 1680 m2
Now, this cost of the canvas height for the tent
= ₹ (1680 × 200)
= ₹ 3,36,000

## 2021

Q1: Water is being pumped out through a circular pipe whose internal diameter is 8 cm. If the rate of flow of water is 80 cm/s. then how many litres of water is being pumped out through this pipe in one hour ?    [2021, 4/5/6 Marks]
Ans:
Given diameter of circular pipe = 8 cm
So, radius of circular pipe = 4cm
Length of flow of water in one sec = 80 cm
length of flow of water in one hour =  80 x 60 x 60 cm=288000 cm=h
Volume of cylinderical pipe in one hour = πr2h

= 14482.28 litre [approx.]
14482.28 litres of water being pumped out through this pipe in 1 hr.

## 2020

Q1:  A solid spherical ball fits exactly inside the cubical box of side 2a. The volume of the ball is
(a)

(b)
(c)
(d)       [2020, 1 Mark]
Ans:
(d)
Diameter of sphere = Distance between opposite faces of cube = 2a
So, volume of spherical ball =
=

Q2: The radius of a sphere (in cm) whose volume is 12πcm3, is
(a) 3
(b) 3√3
(c) 32/3
(d) 31/3     [2020, 1 Mark]
Ans:
(c)
Let radius of the sphere be r.
According to the question,

Q3: Two cones have their heights in the ratio 1: 3 and radii in the ratio 3 : 1 . What is the ratio of their volumes?    [2020, 1 Mark]
Ans:
Let height of one cone be h and height of another cone be 3h. Radius, of one cone is 3r and radius of another cone is r.
∴ Ratio o f their volumes =
= 3 : 1

Q4: How many cubes of side 2 cm can be made from a solid cube of side 10 cm?    [2020, 2 Marks]
Ans:
Let n be the number of solid cubes of  2cm made from a solid cube of side 10 cm.

∴ n x Volume of one small cube = Volume of big cube
⇒ n x (2)3 = (10)3
⇒ 8n = 1000
⇒ n = 1000/8
= 125
Thus, the number of solid cubes formed of side 2 cm each is 125.

Q5: A cone and a cylinder have the same radii but the height of the cone is 3 times that of the cylinder. Find the ratio of their volumes.     [2020, 2 Marks]
Ans: Let the radius and the height of the cylinder are r and h respectively.
So, radios of t he cone is r and height of the cone is 3h.
∴ Volume of the cylinder = πr2h
So Volume of cone =
So, require ratio =
= 1 : 1

Q6: A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form a platform. Find the height of the platform. (Take π = 22/7)   [2020, 4/5/6 Marks]
Ans:
Given that, the depth of the well is 14 m and the diameter is 3 m.
The width of the circular ring of the embankment is 4 m.
A figure is drawn below to visualize the shapes.

From the above figure, we can observe that the shape of the well will be cylindrical, and earth evenly spread out to form an embankment around the well in a circular ring will be cylindrical in shape (Hollow cylinder) having outer and inner radius.
Volume of the earth taken out from well = Volume of the earth used to form the embankment
Hence, Volume of the cylindrical well = Volume of the hollow cylindrical embankment
Let us find the volume of the hollow cylindrical embankment by subtracting volume of inner cylinder from volume of the outer cylinder.
Volume of the cylinder = πr²h where r and h are the radius and height of the cylinder respectively.
Depth of the cylindrical well, = h₁ = 14 m
Radius of the cylindrical well, = r = 3/2 m = 1.5 m
Width of embankment = 4 m
Inner radius of the embankment, r = 3/2 m = 1.5 m
R = 1.5 m + 4 m
= 5.5 m
Let the height of embankment be h
Volume of the cylindrical well = Volume of the hollow cylindrical embankment
πr²h₁ = πR²h - πr²h
πr²h₁ = πh (R² - r²)
r²h₁ = h (R - r )(R + r)
h = [(r²h₁)/(R - r)(R + r)]
h = [((1.5 m)² × 14 m)/(5.5 m - 1.5 m)(5.5 m + 1.5 m)]
= (2.25 m² × 14 m)/(4m × 7 m)
= 1.125 m
Therefore, the height of the embankment will be 1.125 m.

Q7: In Figure-4, a solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Deter mine the volume of the toy. [Take π = 3.14]     [2020, 4/5/6 Marks]
Ans:
Given diameter of conical part = Diameter of hemispherical part = 4cm
∴ Radios of conical part (r) = Radius of hemispherical part (r) = 4/2 = 2 cm
Height of conical part (h) = 2 cm
∴ Volume of toy = Volume of hemisphere + volume of cone

= 3 .14 x 4(1.33 + 0.66)= 3.14 x 4 x 1.99 cm3
Volume of the toy = 24.99 cm3

Q8: A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy. (Use π = 22/7 and √149 = 12.2)   [2020, 4/5/6 Marks]
Ans: Radius of the cone = Radius of the hemisphere = r = 7cm
Height of the cone, h = 10 cm
Now, volume of the toy = volume of hemisphere + volume of cone

=
=  1232 cm3
Curved surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere
= πrl + 2πr2

= 22(12.2 + 14)
= 22 x 26.2
= 576.4 cm3

## 2019

Q1: A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use π = 22/7).       [2019, 3 Marks]
Ans:
Radius of cylinderical part (r) = Radius of each spherical part(r) = 7/2 cm
Height of cylinderical part (h) = 20 - 7/2 - 7/2 = 13 cm
Now. Volume of the solid = Volume of cylinderical part + Volume of two hemispherical endsVolume of the solid =

Volume of the solid = 680.17 cm3.

Q2: A juice seller was serving his customers r using glasses as shown in the given figure. The inner diameter of the  cylindrical glass was 5 cm but bottom of the glass had a hemispherical raised  portion which reduced the capacity of the glass. lf the height of the glass was 10 cm, find the apparent and actual capacity of the glass {Use π = 3.14)       [2019, 3 Marks]

Ans:
Base radius = 5/2 = 2.5 cm
Apparent capacity of glass = Volume of cylindrical portion
= πr2h
= 3.14 x (2.5)2 x 10
= 196.25 cm3
Actual capacity of the glass = Volume of cylinder - Volume of hemisphere

= 196.25 - 32.71
= 163.54 cm3

The document Class 10 Maths Chapter 12 Previous Year Questions - Surface Area and Volumes is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Class 10 Maths Chapter 12 Previous Year Questions - Surface Area and Volumes

 1. What is the formula to calculate the surface area of a cube?
Ans. The formula to calculate the surface area of a cube is 6 x (side)², where side represents the length of one side of the cube.
 2. How do you find the surface area of a cylinder?
Ans. The formula to calculate the surface area of a cylinder is 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.
 3. What is the surface area of a sphere formula?
Ans. The formula to calculate the surface area of a sphere is 4πr², where r is the radius of the sphere.
 4. How can we find the total surface area of a cuboid?
Ans. To find the total surface area of a cuboid, we add the areas of all its faces. The formula is 2(lw + lh + wh), where l, w, and h are the length, width, and height of the cuboid respectively.
 5. How do you calculate the lateral surface area of a cone?
Ans. The formula to calculate the lateral surface area of a cone is πrℓ, where r is the radius of the base and ℓ is the slant height of the cone.

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