Question

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 rete of Rs.40
per litere . (Pie = 22/7).​

Answer 1

Answer:

Let R and r be the radii of the top and base of the bucket respectively,

Let h be its height. Then, we have R = 20 cm, r = 10 cm, h = 30 cm

Capacity of the bucket = Volume of the frustum of the cone

= 1/3 π(R2 + r2 + R r )h = 1/3 π(202 + 102 + 20 x 10 ) x 30 = 3.14 x 10 (400 + 100 + 200) = 21980 cm3 = 21.98 litres Now,

Surface area of the bucket = CSA of the bucket + Surface area of the bottom

= π l (R + r) + πr2 We know that, l = √h2 + (R – r)2 = √[302 + (20 – 10)2] = √(900 + 100) = √1000 = 31.62 cm So, The Surface area of the bucket = (3.14) x 31.62 x (20 + 10) + (3.14) x 102 = 2978.60 + 314 = 3292.60 cm2 Next, given that the cost of 1 litre milk = Rs 25 Thus,

the cost of 21.98 litres of milk = Rs (25 x 21.98) = Rs 549.50

Answer 2

Answer:

Let R and r be the radii of the top and base of the bucket respectively,

Let h be its height. Then, we have R = 20 cm, r = 10 cm, h = 30 cm

Capacity of the bucket = Volume of the frustum of the cone

= 1/3 π(R2 + r2 + R r )h = 1/3 π(202 + 102 + 20 x 10 ) x 30 = 3.14 x 10 (400 + 100 + 200) = 21980 cm3 = 21.98 litres Now,

Surface area of the bucket = CSA of the bucket + Surface area of the bottom

= π l (R + r) + πr2 We know that, l = √h2 + (R – r)2 = √[302 + (20 – 10)2] = √(900 + 100) = √1000 = 31.62 cm So, The Surface area of the bucket = (3.14) x 31.62 x (20 + 10) + (3.14) x 102 = 2978.60 + 314 = 3292.60 cm2 Next, given that the cost of 1 litre milk = Rs 25 Thus,

the cost of 21.98 litres of milk = Rs (25 x 21.98) = Rs 549.50