Question

What will be the ratio of the total surface area of the cone to the total surface area of the sphere if, slant height of the cone is equal to the diameter of the base of the cone and radius of the cone is equal to radius of the sphere?

• A. 3:4
• B. 4:3
• C. 3:2
• D. 2:3

Answer 1

The correct option is A 3:4

Given that,
Slant height of cone
= Diameter of the cone
$\Rightarrow l=2\times r$

We know that,
Total surface area of sphere
$=4\pi r^2$

Total surface area of cone
$=\pi rl+\pi r^2$

Now,
$=\frac{TSAofcone}{TSAofsphere}$

$=\frac{\pi rl+\pi r^2}{4\pi r^2}$

$=\frac{3\pi r^2}{4\pi r^2}$

[ $usingl=2r$]

$=\frac{3}{4}$

$=3:4$