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A bucket is 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 and surface area of the bucket. Also, find the cost of milk which can completely fill the container, at the rate of Rs 25 per litre (use π = 3.14)

Solution:

Given, a bucket is in the form of a frustum of a cone.

The height of the bucket is 30 cm

The radii of its lower and upper ends are 10 cm and 20 cm.

We have to find the capacity and surface area of the bucket.

We have to find the cost of milk which can completely fill the container, at the rate of Rs. 25 per litre.

Volume of frustum of a cone = πh/3 [R² + r² + Rr]

Given, R = 20 cm

r = 10 cm

h = 30 cm

Volume of bucket = (3.14)(30/3)[(20)² + (10)² + 20(10)]

= (3.14)(10)[400 + 100 + 200]

= (3.14)(10)[700]

= (3.14)(7000)

= (3.14)(7)(1000)

= 21.98(1000) cm³

= 21.98 litres

Cost of 1 litre milk = Rs. 25

Cost of 21.98 litres of milk = 25(21.98)

= Rs. 549.50/-

Therefore, the cost of milk which can completely fill the container is Rs. 549.50/-

Surface area of the bucket = curved surface area of the bucket + area of base

Curved surface area of frustum of a cone = π(R+r)l

Slant height, l = √h² + (R - r)²

l = √30² + (20 - 10)²

= √900 + 100

= √1000

l = 31.62 cm

Curved surface area = (3.14)(20 + 10)(31.62)

= (3.14)(30)(31.62)

= 2978.604 cm²

Area of base = πr²

= (3.14)(10)²

= (3.14)(100)

= 314 cm²

Surface area of the bucket = 2978.604 + 314

= 3292.604 cm²

Therefore, the surface area of the bucket is 3292.604 cm².

✦ Try This: A bucket is in the form of a frustum of a cone of height 20 cm with radii of its lower and upper ends as 12 cm and 18 cm, respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the container, at the rate of Rs 15 per litre (use π = 3.14).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Sample Problem 1

A bucket is 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 and surface area of the bucket. Also, find the cost of milk which can completely fill the container, at the rate of Rs 25 per litre (use π = 3.14)

Summary:

A bucket is 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. The capacity and surface area of the bucket are 21980 cm³ and 3292.604 cm². Also, the cost of milk which can completely fill the container, at the rate of Rs 25 per litre is Rs.549.50/-

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