The material of solid cone is converted into the shape of solid cylinder of equal radius. If the height of the cylinder is 6 cm, what is the height of the cone?
Solution
Correct Answer: Option E
Since radius of the solid cone is equal to the radius of the solid cylinder and height of the cylinder (h) given is 6 cm
∴ Volume of the solid cone is given by \(= \frac{1}{3}\pi {R^2}h\)
∴ Volume of the solid cylinder is given by \(= \pi {r^2}h\)
Since material of solid cone is converted into the shape of solid cylinder
∴ Volume of the solid cone = Volume of the solid cylinder
\(\therefore {\rm{\;}}\frac{1}{3}\pi {R^2}H = {\rm{\;}}\pi {r^2}h{\rm{\;}}\) [∵ R = r]
∴ H = 3h
∴ H = 3 × 6 =18 cm
∴ Height of the cone (h) = 18 cm
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions