Question

My teacher says one its wrong witch on is it?

Answer 1

`\begin{gathered} V=835.59\text{ m}^3 \\ S.A.=547.11\text{ m}^2 \end{gathered}`

Step-by-step explanation:

Given:

Radius(r) = 7.2 m

Slant height(l) = 17 m

To find:

The volume and surface area

Let's go ahead and determine the height(h) of the cone using the Pythagorean theorem as seen below;

`\begin{gathered} l^2=h^2+r^2 \\ 17^2=h^2+7.2^2 \\ 289=h^2+51.84 \\ h^2=289-51.84 \\ h^2=237.19 \\ h=√(237.19) \\ h=15.4\text{ m} \end{gathered}`

So the height(h) of the cone is 15.4 m

Let's go ahead and solve for the Volume(V) of the cone using the below formula;

`\begin{gathered} V=(\pi r^2h)/(3) \\ =(3.14*7.2^2*15.4)/(3) \\ =835.59\text{ m}^3 \end{gathered}`

So the volume of the cone is 835.59 m^3

We can go ahead and determine the surface area(S.A.) of the cone as seen below;

`\begin{gathered} S.A.=\pi r^2+\pi rl \\ =\pi r(r+l) \\ =3.14*7.2(7.2+17) \\ =22.608(24.2) \\ =547.11\text{ m}^3 \end{gathered}`

So the surface area of the cone is 547.11 m^2