Question

If the surface area of the cone below is 628.32, find its volume. (Diameter is 16)

Answer 1

To solve the question given

We will follow the steps below

First, the surface area is given to be 628.32

diameter = 16 this implies that radius = d/2 = 16/2 = 8

First, using the formula

surface area of a cone = πr² + πrl

we will find l

remember that π= 3.14

substituting the values into the above formula

surface area of a cone = πr² + πrl

628.32 = 3.14(8)² + 3.14(8)l

Next is to solve for l

628.32 = 200.96 +25.12 l

subtract 200.96 from both-side of the equation

628.32 - 200.96= 200.96 - 200.96 +25.12 l

427.36 = 25.12 l

Divide both-side of the equation by 25.12

427.36/25.12 = 25.12 l/25.12

17.01 = l

slant height (l) = 17.01

We can now calculate the volume of the cone using the formula:

$V\text{ = }\frac{1}{3}\pi r^2\sqrt{l^2-r^2}$

substituting r=8 π = 3.14 and l = 17.01 in the above formula

$V=\frac{1}{3}\text{ }\times3.14\times(8)^2\text{ }\times\sqrt{(17.01)^2-(8)^2}$

$V=\text{ }\frac{1}{3\text{ }}\times3.14\times64\text{ }\times\sqrt{289.3401\text{ - 64}}$

$V=\text{ }\frac{1}{3}\times200.96\text{ }\times\sqrt{225.3401}$

$V\text{ =}\frac{1}{3}\times\text{ 200.96}\times15.01$$V\text{ = }\frac{3016.4096}{3}$

V=1005.47

Volume of the cone is 1 005.47