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 .

E M B I B E

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

HARD

10th CBSE

IMPORTANT

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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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Important Questions on Surface Areas and Volumes

MEDIUM

10th CBSE

IMPORTANT

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.

EASY

10th CBSE

IMPORTANT

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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