Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

The document Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Q1. A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how much water can the bucket hold?

[use π = 22/7]

Sol. Here  Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Height h = 15 cm
Since the volume of a frustum of a cone

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

∴ Volume of the bucket

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Q2. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27th of the volume of the given cone, at what height above the base is the section made?

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Sol. In the figure, we have ΔABC ~ ΔADE

[By AA similarity]

⇒ Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

[∵ corresponding sides of similar Δs are proportional.]

⇒ Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev     ...(1)
Here, volume of the small cone = Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Volume of the given cone =  Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Since, [Volume of the small cone] = 1/27 
[Volume of the given cone]

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

∴The required height BD = AD − AB = (30 − 10) cm = 20 cm

Q3. A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the altitude of the cone is divided by the plane.

Sol. In the figure, we have

ΔABC ~ ΔADE    [AA similarity]

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

[ä sides of similar Δs are proportional.]

⇒ Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Now, curved surface area of the small cone = πrl
Curved surface area of the whole cone = πRL Since,
[Surface area of the remainder (frustum)]

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

=  8/9 [curved surface area of the given cone]

∴ [curved surface area of the frustum]

= 8/9 [curved surface area of the given cone]
⇒ [curved surface area of the small cone]

= 1/9 [curved surface area of the whole cone]

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Now, BD = H − h = 3h − h = 2h

∴ Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

⇒ AB : BD = 1 : 2

Q4. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent.

[Use π = 22/7]

Sol. For cylindrical part:

We have, radius (r) = 52.5 m
Height (h)=3 m
Curved surface area = 2πrh
For the conical part
Slant height (l) = 53 m
Radius (r) = 52.5 m
∴Curved surface area = πrl
Area of the canvas = 2πrh + πrl
= πr (2h + l)

  Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRevLong Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

= 11 × 15 × 59 m2 =  9735 m2

Q5. Find the number of coins of 1.5 cm diameter and 0.2 cm thickness to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Sol. The coin is in a cylindrical form,
∴ Volume of the coin

  Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Let the number of coins= n
∴Total volume of all coins

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Q6. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part in 36 cm high. Find the weight of the pillar if one cu. cm of iron weighs 7.8 grams.

Sol. Here, height of the cylindrical part h = 240 cm
Height of the conical part, H = 36 cm
Radius r =8 cm
Now, the total volume of the pillar

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Q7. An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. Find the cost of oil which can completely fill the container at the rate of Rs 50 per litre. Also, find the cost of metal used, if it costs Rs 5 per 100 cm2.

[Use π = 3.14]

Sol. Here, for the frustum,

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

∴ Volume of the container

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

= 1.30624 litres ≈ 1.31 approx.

Cost of oil = Rs (1.31 × 50) = Rs 65.50

Now, the total surface area of the container (excluding upper base)

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Q8. The perimeters of the ends of frustum of a cone are 207.24 cm and 169.56 cm. If the height of the frustum be 8 cm , find the whole surface area of the frustum. [Use π = 3.14]

Sol. Let the radii of circular ends be R and r [ R > r]
Perimeter of circular ends are 207.24 cm and 169.56 cm
∴ 2 π R = 207.24

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Slant-height of the frustum

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

The whole surface area of the frustum = π [(R2 + r2) + (R + r)l]
∵ Required whole surface area of the frustum

= 3.14 [332 + 272 +
(33 + 27) × 10] cm2
= 3.14 [1089+ 729 + 600] cm2
= 3.14 [2418] cm2  =  7592.52 cm2

Q9. A building is in the form of a cylinder surmounted by a hemispherical dome as shown in the figure. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the height of the building, if it contains  Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev of air.

Sol. Here, radius of the hemispherical part = r (say)

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Let the total height of the building = h
And the height of the cylindrical part = H

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRevLong Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
But, volume of the air in the building

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Thus, the required height of the building is 6 metres.

Q10. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and diameter of the base is 8 cm. Determine the volume of the toy. If the cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also, find the total surface area of the toy.

Sol. Let the radius of the hemisphere = r
And height of the cone = h

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRevLong Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Since, the cube circumscribing the given solid must have its edge as (4 + 4) cm i.e., 8 cm,
∴ Volume of the cube =(edge)3 = (8)3 cm3 = 512 cm3
Now, difference in volumes of the cube and the toy

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Also, total surface area of the toy

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRevLong Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev
Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

Summary

,

practice quizzes

,

Viva Questions

,

past year papers

,

Previous Year Questions with Solutions

,

pdf

,

video lectures

,

Extra Questions

,

study material

,

Objective type Questions

,

Free

,

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

,

Important questions

,

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

,

shortcuts and tricks

,

Long Answer Type Questions- Surface Areas and Volumes Class 10 Notes | EduRev

,

ppt

,

Exam

,

Semester Notes

,

MCQs

,

mock tests for examination

,

Sample Paper

;