Question

Please help me with this please ASAP ASAP please ASAP

Answer 1

Given:

The diagram of a cone.

To find:

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

Solution:

From the given diagram, we get

Radius of the cone = 6

Slant height of the cone = 10

Suppose $h$ be the height of the cone.

According to Pythagoras theorem:

$hypotenuse^2=Perpendicular^2+Base^2$

Using the 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:

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

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

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

$V=96\pi$

Hence, 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.