The volume of hemisphere is 2425 1 2 cm 3 . Find its curved surface area.

Let r be the radius of the hemisphere. Given, Volume of hemisphere = 2425 1 2 cm 3 = 4851 2 cm 3 ⇒ 2 3 πr 3 = 4851 2 ⇒ 2 3 × 22 7 × r 3 = 4851 2 ⇒ 44 21 × r 3 = 4851 2 ⇒ r 3 = 4851 × 21 88 ⇒ r 3 = 4851 × 21 88 ⇒ r = 1157 . 625 3 ⇒ r = 10 . 5 cm Now, Curved surface area of hemisphere = 2 πr 2 = 2 × 22 7 × ( 10 . 5 ) 2 = 44 7 × 110 . 25 = 693 cm 2 Hence, curved surface area of hemisphere is 693 cm 2 .

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 .