Question

A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill a container at the rate of ₹ 40 per litre.

Answer 1

Height of the frustum (h) = 16 cm

Radius of the upper part (R) = 20 cm

Radius of the lower part (r) = 8 cm

Volume of the frustum

= `1/3 pi"h" ["R"^2 + "r"^2 + "Rr"]` cu.units

= `1/3 xx 22/7 xx 16 [20^2 + 8^2 + 20 xx 8]` cu.units

= `1/3 xx 22/7 xx 16 [400 + 64 + 160]` cu.units

= `(22 xx 16 xx 624)/(3 xx 7) "cm"^3`

= `(22 xx 16 xx 208)/7 "cm"^3`

= `73216/7`

= 10459.43 cm³

= `10459.43/1000 "litre"`

= 10.45943 litre

= 10.459 litre

Cost of milk in the container = 10.459 × 40 = ₹ 418.36

Cost of the milk = ₹ 418.36