Question

The area of the base of the cone is 64π square millimeters, and the area of the lateral surface is 112π square millimeters. Find the radius r and slant height ℓ of the cone.

Answer 1

Answer:

Radius = 8 mm

Slant Height = 14 mm

Step-by-step explanation:

Base of a cone is a circle.

Area of circle is given as $A=\pi r^{2}$

Where $r$ is the radius.

Given that

$A = 64 \pi\ mm^2\\\Rightarrow \pi r^{2} = 64\pi \\\Rightarrow r^{2} = 64\\\Rightarrow r = 8\ mm$

Hence, radius is 8 mm.

Formula for Lateral Surface Area of a cone:

$LSA = \pi rl$

Where $r$ is the radius and

$l$ is the slant height of cone

Given that $LSA = 112 \pi\ mm^2$

$\Rightarrow 112\pi = \pi \times 8 \times l\\\Rightarrow 8 \times l = 112\\\Rightarrow l = 14\ mm$

Hence, slant height is 14 mm