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 .

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From a solid cylinder of height $2.8 cm$ and diameter $4.2 cm$ , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of remaining solid?

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Important Questions on Surface Areas and Volumes

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10th CBSE

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.1>Q 7

Two cones of the same base radius

8 cm

and height

15 cm

are joined together along their bases. Find the surface area of the shape so formed?

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.1>Q 8

A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and the diameter of the cylinder part are

21 cm and 40 cm

respectively, and the height of the cone is

15 cm

, then find the total surface area of the toy. Take

π = 3.14 .

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.1>Q 9

A toy is in the form of a cone of radius

3.5 cm

mounted on a hemisphere of base diameter

7 cm

. If the total height of the toy is

15.5 cm

, find the total surface area of the toy.

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.1>Q 10

In the adjoining figure, a sphere is inscribed in a cylinder, prove that the surface of the sphere is equal to the inner curved surface of the cylinder.

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.1>Q 11

A military tent of height

8.25 m

is in the form of a right circular cylinder of base diameter

30 m

and height

5.5 m

surmounted by a right circular cone of same base radius. Find the length of the canvas used in making the tent, if the breadth of the canvas is

1.5 m

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.2>Q 1

If the volume and the (curved) surface area of a hemisphere are numerically equal, then what is the length of diameter of hemisphere?

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.2>Q 2

Two cubes have their volume in the ratio

1 : 27

. Find the ratio of their surface areas.

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10th CBSE

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CBSE Syllabus Standard Mathematics for Class X>Chapter 14 - Surface Areas and Volumes>Exercise 14.2>Q 3

If the radii of the bases of a cylinder and cone are in the ratio

3 : 4

and heights are in the ratio

2 : 3

, then what is the ratio of their volumes?

From a solid cylinder of height 2.8cm and diameter 4.2cm, a conical cavity of same height and same diameter is hollowed out. Find the total surface area of remaining solid?

Important Questions on Surface Areas and Volumes

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From a solid cylinder of height $2.8 cm$ and diameter $4.2 cm$ , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of remaining solid?