Surface Areas and Volume Class 9 Worksheet Maths

Multiple Choice Questions

Q1: The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of  our walls of room?
(a) 636 m²
(b) 516 m²
(c) 800 m²
(d) 456 m²
Ans: (b)
Area of the walls is given by = 2(BH + LH) + LB = 2(90 + 108) + 120 = 516 m² 

Q2: The plastic paint in an Asian paint container is sufficient to paint an area equal to 93.75m². How many blocks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container
(a) 100
(b) 800
(c) 940
(d) 1000
Ans: (d)
Total surface area of one block = 2(lb + bh + lh)
= [2(22.5 × 10 + 10 × 7.5 + 22.5 × 7.5)] cm
= 2(225 + 75 + 168.75) cm²
= (2 × 468.75) cm²
= 937.5 cm²
Let n blocks can be painted out by the paint of the container.
Area of n bricks = (n ×937.5) cm² = 937.5n cm²
Area that can be painted by the paint of the container = 93.75 m² = 937500 cm²
937500 = 937.5n
n = 1000
Therefore, 1000 blocks can be painted out by the paint of the container.

Q3: Curved surface area of a cone is 308 cm² and its slant height is 14 cm.
(a) Radius of the cone is 7 cm
(b) total surface area is 462 cm²
(c) Height of the cone is √147 cm
(d) None of the above
Ans: (a),(b),(c)
Curved surface area = πrl
So r = 7 cm
Now total surface area = πr² + πrl = 462 cm² 

Q4: Sita had to make a model of cylindrical kaleidoscope for her science project. She wanted to use black chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 30cm with a 2.7 cm radius? (Use p = 22/7)
(a)1320 cm²
(b) 1400 cm²
(c) 986 cm²
(d) None of these
Ans: (a)
Curved surface of cylinder = 2πrh

Q5: The radii of two cones are in the ratio of 2:3 and their heights are in the ratio of 7:3. The ratio of their volumes is
(a) 20:27
(b) 28:27
(c) 28:27
(d) None of these
Ans: (c)
Volume = (1/3)πr²h

Q6: Find the maximum length of the rod that can be kept in cuboidal box of sides 30cm, 20cm and 10cm.
(a)
(b)
(c)
(d) None of these
Ans: (a)
Diagonal is the longest length in the cuboid so

Q7: A box is made entirely of glass panes (including base) held together with tape. It is 3 cm long, 2.5 cm wide and 2.5 cm high. How much of tape is needed for all the 12 edges?
(a) 30cm
(b) 32cm
(c) 40 cm
(d) None of these
Ans: (b)
Length of tape=4( L+B+H)=32 cm

Fill in the blank

Q1: A cylinder radius is doubled and height is halved, the curved surface area of the cylinder will ____ (Increase/decrease/remain same)
Ans: Remain same
CSA= 2πrh
So if r is doubled, h is halved,CSA will remain same

Q2: The radius of the sphere is 7 cm, the surface area of the sphere is____ (616 cm² / 700 cm²/ 800 cm²)
Ans: 616 cm²,  Surface area = 4πr²

Q3: Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a big cube. The volume of the big cube is ___ (1800cm³/1728 cm³)
Ans: 1728 cm³, V = V₁ + V₂ + V₃ = 6³ + 8³ + 10³

Q4: The total surface area of a hemisphere of radius 10 cm using value of π = 3.14 is _____(956 cm²/942 cm²)
Ans: 956 cm², Total surface area = 3πr²

Q5: A right circular cylinder just encloses a sphere of radius. The ratio of there surface area is ______ (1:1 / 1:2)
Ans: 1:1 In this height of cylinder will be 2r and radius of cylinder will r. So it is equal

Q6: The lateral surface area of a cube is 256 m², the volume is ____ (456 m³/512 m³)
Ans: 512 m³, Lateral surface area = 4a² and Volume = a³c

True / False

Q1: A cylinder, hemisphere and cone stand on equal base and same height, the Volume ratio is 3:2:1
Ans: True. All of them will have height as r as hemisphere height can be r only. For cylinder = πr³
Hemisphere = (2/3) πr³
Cone = (1/3) πr³
So ratio is 3:2:1

Q2: The radius of a solid sphere is 24 cm. 8 spheres can be made from it of 12cm radius
Ans: True. Sphere volume =(4/3) πr³

Q3: radius of the cone is doubled and height is halved, the volume will be halved
Ans: False. Volume will be doubled. Volume is given by =(1/3)πr²h

Q4: A river 10m deep and 40m wide is flowing at the rate of 2m per min. 48000m³ water will flow into the sea from river
Ans: True. It is equal to the volume of the cuboid  10m,40m,and 120 m

Q5: A cylinder radius is halved and height is doubled, the volume will become halved
Ans: True.

Q6: The side of the cube is 4 cm, the diagonal length is  cm
Ans: False

Subjective Type Questions

Q1: Ramesh has build a cuboidal water tank with lid for his house with each outer edge 1.5m long. He gets the outer surface of tank excluding the base, covered with square tiles of side 25cm. Find how much he would spend for tiles, if cost of the tile is Rs 400 per dozen.
Ans: Surface Area of the cuboidal water tank where tiles to be placed= 5L2= 11.25 m²
Area of 1 Tile= 25² = 625 cm² = .0625 m²
No of Tiles required=11.25/.0625 = 180 = 15 dozen
Cost of tiles will be = 400 * 15 = Rs 6000

Q2: The diameter of a roller are 84cm and its length is 120cm. It takes 500 complete revolutions to move once more over to level a playground. Find area of playground in m²?
Ans:  Diameter =84 cm, Therefore radius=42 cm Curved Surface area of cylinder=
 = 31680 cm² = 3.1680 m² 
Area of playground = 500 × 3.1680 = 1584 m² 

Q3: In a hot water heating system, there is a cylindrical pipe of length 28m and diameter 5cm. Find the total radiating surface in system?
Ans: Diameter = 5 cm, Therefore radius = 2.5 cm
Curved Surface area of cylinder is the radiating surface=


Q4: Three cubes of each side 4cm are joining end to end. Find the surface area of resulting cuboid
Ans:
Surface of the cuboid will be = 4 × 4 × 12 + 2 × 4 × 4 = 224 cm² 

Q5: A river 3m deep and 40m wide is flowing at the rate of 2km/hr. How much water will fall into the sea in a minute?
Ans: Speed of water in a river = 2 km/hr
Length of flow of water in 1 minute

Therefore Volume of water

Volume in litres= 4000 * 1000= 4 × 10⁶ 

Q6: The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20cm and height 10m. How much concrete mixture would be required to build 14 such pillars?
Ans: Volume of single pillar= πr²h = .2π
Volume of 14 Pillars= 14 × .2 π = 8.8 m³