A bucket in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm , respectively. Find the capacity of the bucket. Also find the cost of milk which can completely fill the bucket at the rate of ₹ 40 per litre. Use π = 22 7

Given that, a bucket in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm , respectively. Capacity of the bucket can be obtained by finding the volume of the frustum of cone. We know that, volume of the frustum of cone = 1 3 πh r 1 2 + r 2 2 + r 1 r 2 Where, h is the height the frustum of the cone, r 1 , r 2 are the radii of both ends of the frustum. Using the formula mentioned above, Capacity = 1 3 × 22 7 × 30 20 2 + 10 2 + 20 × 10 = 22 7 × 10 400 + 100 + 200 = 22 7 × 10 × 700 = 22 × 10 × 100 = 22000 cm 3 = 22 litre [ ∵ 1 litre = 1000 cm 3 ] Cost of 22 litre milk = Cost of 1 litre milk × 22 = ₹ 40 × 22 = ₹ 880 Hence, the capacity of the bucket is 22 litre and the cost of milk is ₹ 880 .

MEDIUM

10th CBSE

IMPORTANT

Earn 100

The figure given below, shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.

Important Questions on Surface Areas and Volumes

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 2

The figure given below shows a solid trophy made of shining glass. If one cubic centimetre of glass costs $₹ 0.75$ , find the cost of the glass for making the trophy.

Question Image

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 3

From a solid cylinder of height

15 cm

and diameter

16 cm

, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use

π = 3.14

)

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 4

A toy is in the form of a cone mounted on a hemisphere of same radius

7 cm

. If the total height of the toy is

31 cm

, find its total surface area.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 5

The entire surface of a solid cone of base radius

3 cm

and height

4 cm

is equal to the entire surface of a solid right circular cylinder of diameter

4 cm

. Find the ratio of their curved surfaces.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 5

The entire surface of a solid cone of base radius

3 cm

and height

4 cm

is equal to the entire surface of a solid right circular cylinder of diameter

4 cm

. Find the ratio of their volumes.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 6

A medicine capsule is in the shape of a cylinder of diameter

0.5 cm

with two hemispheres stuck to each of its ends. The length of the entire capsule is

2 cm

. Find the capacity of the capsule.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 7

How many lead shots each of diameter

4.2 cm

can be obtained from a solid rectangular lead piece with dimensions

66 cm, 42 cm

and

21 cm

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Chapter Test>Q 8

Find the least number of coins of diameter

2.5 cm

and height

3 mm

which are to be melted to form a solid cylinder of radius

3 cm

and height

5 cm

The figure given below, shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.

Important Questions on Surface Areas and Volumes

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