1 Answer

Tehaaron · Answer 1 · 2021-01-31T15:42:43+0000

Given:

The base area of a right circular cone is
(1)/(4) of its total surface area.

To find:

The ratio of the radius to the slant height.

Solution:

We know that,

Area of base of a right circular cone =
$\pi r^2$

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

where, r is radius and l is slant height.

According to the question,

$\pi r^2=(1)/(4)(\pi rl+\pi r^2)$

Multiply both sides by.

$4\pi r^2=\pi rl+\pi r^2$

$4\pi r^2-\pi r^2=\pi rl$

$3\pi r^2=\pi rl$

Cancel out the common factors from both sides.

3r=l

Now, ratio of the radius to the slant height is

(r)/(l)=(r)/(3r)

(r)/(l)=(1)/(3)

Therefore, the ratio of the radius to the slant height is 1:3.

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