Question 39

A cylindrical vessel of height 9 cm and radius 7 cm is completely ﬁlled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

Solution

Let height of cone = $$h$$ cm and radius, r = 10 cm

Height of cylinder, H = 9 cm and Radius, R = 7 cm

Volume of cylinder = Volume of cone

=> $$\pi R^2 H = \frac{1}{3} \pi r^2 h$$

=> $$(7)^2 \times 9 = \frac{1}{3} \times (10)^2 \times h$$

=> $$h = \frac{49 \times 9 \times 3}{100} = \frac{1323}{100}$$

=> $$h = 13.23$$ cm

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: