Question

A well 28.8 m deep and of diameter 2 m is dug up. The soil dug out is spread all around the well to make a platform 1 m high considering the fact losse soil settled to a height in the ratio 6 : 5 find the width of the platform.

Answer 1

Volume of Soil drug out = π (1)² (28.8) cu m.

∴ Volume of soil that would be settled on the platform is ${\displaystyle \frac{5\times \pi \times 28.8}{6}}$ cu. m.

Let the width of the platform be r cm. Then, 
π(1 + r²) - (1)² (1) = ${\displaystyle \frac{5\times \pi \times 28.8}{6}}$

⇒ (1 + r)² - 1 = ${\displaystyle \frac{5\times 28.8}{6}}$ = 24

⇒ (1 + r)² = 25
⇒ 1 + r = 5
⇒ r = 5 - 1
⇒ r = 4 cm.