Question

Which of the following is false for a cone?

• A. Volume of cylinder is twice that of volume of cone of same height and radius
• B. Slant height is required to find the curved surface area of cone
• C. Total surface area = $\pi$rl + $\pi$$r^2$
• D. None of these

Answer 1

The correct option is A

Volume of cylinder is twice that of volume of cone of same height and radius

Volume of cylinder having height 'H' and radius 'R' = $\pi (R{)}^{2}H$

Volume of cone having same height 'H' and radius 'R' = $\frac{1}{3}\pi (R{)}^{2}H$

So, we can see that for same radius and height, the volume of a cylinder is thrice that of a cone.

The curved surface area of a cone is equal to $\pi rl$ where 'l' is equal to slant height.

Total surface area of a cone = Curved surface area + Area of a base of the cone
= $\pi rl+\pi r^2$, where 'r' = Radius of the base of cone and 'l' = Slant height of the cone.