​ A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 {3/7} cm^3. ​

Question

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 \(\frac{3}7\) cm³. The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs. 1.40 per cm²

Answer 1

Given: 

volume of the frustum = 10459 \(\frac{3}7\) cm³ 

Radii of lower and upper ends resp.: r’ = 8 cm and r’’ = 20 cm

Volume = \(\frac{1}3π(r'^2 + r"^2 + r'r")h\)

⇒ \(\frac{1}3π(8^2 + 20^2 + 8\times20)\times{h}\) = 10459 \(\frac{3}7\)

⇒ h = 16 cm 

Let slant height be l 

Slant height, l = \(\sqrt{(r' - r")^2 + h^2}\)

⇒ l = \(\sqrt{(20 - 8)^2 + 16^2}\)

⇒ l = 20 cm 

Total surface area of the frustum = π(r’ + r’’)l + πr’² + πr’’² 

= π(20 + 8)20 + π (20)² + π (8)² 

= 3218.29 cm² 

cost of metal sheet used in making the container at the rate of Rs. 1.40 per cm² 

= 3218.28 × 1.40 

= Rs 4506