A container open at the top and made up of a metal sheet,is in the form of a frustum of - Maths - Surface Areas and Volumes

Question

A container open at the top and made up of a metal sheet,is in
the form of a frustum of a cone of height 16cm with radii of its
lower and upper ends as 8cm and 20cm respectively Find the cost of
milk which can completely fill the container at the rate of Rs 20
per litre

Ajanta Trivedi · Accepted Answer

radius of the upper end of the container R =20 cm

radius of the lower end of the container r = 8 cm

container is in the shape of the frustum.

height of the frustum h =16 cm

volume of the container (frustum) V= $\frac{1}{3} π h (R^{2} + r^{2} + R r) = \frac{1}{3} * \frac{22}{7} * 16 * (20^{2} + 8^{2} + 20 * 8)$

V= $\frac{22 * 16}{21} * (400 + 64 + 160) = \frac{352}{21} * 624 = 10459.4286 c m^{3}$

amount of the milk to fill the container = volume of the container

since $1 c m^{3} = 0.001 l i t r e$

amount of the milk to fill the container =10.46 litre

total cost of the milk =10.46*20=209.20 /-

A container open at the top and made up of a metal sheet,is in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends as 8cm and 20cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 20 per litre..