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

A solid right circular cone of diameter $14 cm$ and height $8 cm$ is melted to form a hollow sphere. If the external diameter of the sphere is $10 cm$ , find the internal diameter of the sphere

Important Questions on Surface Areas and Volumes

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 19

A vessel is in the form of an inverted cone. Its height is

11 cm

and the radius of its top, which is open, is

2.5 cm

. It is filled with water upto the rim. When some lead shots, each of which is a sphere of radius

0.25 cm

, are dropped into the vessel,

\frac{2}{5}

of the water flows out. Find the number of lead shots dropped into the vessel.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 20

The surface area of a solid metallic sphere is

1256 c m^{2}

. It is melted and recast into solid right circular cones of radius

2.5 c m

and height

8 c m

. Calculate the radius of the solid sphere.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 20

The surface area of a solid metallic sphere is

1256 c m^{2}

. It is melted and recast into solid right circular cones of radius

2.5 c m

and height

8 c m

. Calculate the number of cones recast .

(

Use

π = 3.14)

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 21

Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions

1.57 m \times 1.44 m \times 95 cm

. The overhead tank has its radius of

60 cm

and its height is

95 cm

. Find the height of the water left in the sump after the overhead tank has been completely filled with water from a sump which had been full. Compare the capacity of the tank with that of the sump.

(

Use

π = 3.14)

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 22

Water in a canal,

5.4 m

wide and

1.8 m

deep , is flowing with a speed of

25 k m / h o u r .

How much area can it irrigate in

40

minutes , if

10 c m

standing water is required for irrigation.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 23

Water is flowing at the rate of

15 km / h

through a pipe of diameter

14 cm

into a cuboidal pond which is

50 m

long and

44 m

wide. In what time will the level of water in pond rise by

21 cm

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.3>Q 24

Water is flowing through a cylindrical pipe, of internal diameter of

2 c m

, into a cylindrical tank of base radius

40 c m

, at the rate of

0.4 m / s e c

. Determine the rise in the level of water in the tank in half an hour.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.4>Q 1

If the slant height of the frustum of a cone is

6 c m

and the perimeter of its circular bases are

24 c m

and

12 c m

, then find its curved surface area.

A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A solid right circular cone of diameter $14 cm$ and height $8 cm$ is melted to form a hollow sphere. If the external diameter of the sphere is $10 cm$ , find the internal diameter of the sphere