In a rainwater harvesting system, the rainwater from a roof of dimension 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3 . 5 m . If the tank is full, find the rain in c m .

Length of the roof, l = 22 m Breadth of the roof, b = 20 m Let the height of water on the roof be h Radius of the cylindrical vessel, r Height of water in the cylindrical vessel H = 3 . 5 m Volume of water falling on the roof = Volume of water in the cylindrical vessel l b h = π r 2 H 22 × 20 × h = π × 1 2 × 3 . 5 h = 1 40 m = 2 . 5 c m Thus, 2 . 5 c m of rainfall falls on the roof.

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 .