A cone has a circular base of radius 6 mm . Given
that the curved surface area of the cone is ,
find its slant height.

Ask by Vaughan Savage. in Indonesia

Mar 19,2025

Question

A cone has a circular base of radius 6 mm . Given that the curved surface area of the cone is $$ 84 \pi \mathrm{~mm}^{2} $$, find its slant height.

UpStudy AI · Accepted Answer

1. The curved surface area (CSA) of a cone is given by the formula:
   $$
   \text{CSA} = \pi r s
   $$
   where $$ r $$ is the radius of the base and $$ s $$ is the slant height.

2. Given that the radius $$ r = 6 $$ mm and the curved surface area is $$ 84\pi $$ $$\text{mm}^2$$, we have:
   $$
   \pi \times 6 \times s = 84\pi
   $$

3. Divide both sides of the equation by $$\pi$$ to simplify:
   $$
   6s = 84
   $$

4. Solve for $$ s $$:
   $$
   s = \frac{84}{6} = 14 \text{ mm}
   $$

The slant height of the cone is $$ 14 $$ mm.
The slant height of the cone is 14 mm.

A cone has a circular base of radius 6 mm . Given
that the curved surface area of the cone is ,
find its slant height.

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A cone has a circular base of radius 6 mm . Given that the curved surface area of the cone is , find its slant height.