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ladessa [460]
3 years ago
13

Please help me with this ASAP Don’t ANSWER With links please ****

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

Given:

Radius of the cone = 6

Slant height of the cone = 10

To find:

The lateral area, surface area and volume of the cone.

Solution:

Let h be the height of the cone. By Pythagoras theorem, we get

10^2=(6)^2+h^2

100=36+h^2

100-36=h^2

64=h^2

Taking square root on both sides, we get

\sqrt{64}=h

8=h

The lateral area of a cone is:

A_L=\pi rl

A_L=\pi (6)(8)

A_L=48\pi

The surface area of a cone is:

A_S=\pi rl+\pi r^2

A_S=\pi (6)(8)+\pi (6)^2

A_S=48\pi +36\pi

A_S=84\pi

Volume of cone is:

V=\dfrac{1}{3}\pi r^2h

V=\dfrac{1}{3}\pi (6)^2(8)

V=\dfrac{288}{3}\pi

V=96\pi

Therefore, the lateral area of a cone is 48\pi sq. units, the surface area of a cone is 84\pi sq. units and the volume of the cone is 96\pi cubic units.

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