Question

Can you please help me with this the last two tutors couldn’t help me

Answer 1

The answers are :

r = 6√2 or 8.5

h = 17

LA = 906.3

SA = 1358.7

V = 3845.3

EXPLANATION :

From the problem, we have a cylinder.

We need to find the radius first.

If we take out the triangle in the upper portion of the cylinder.

We will have an isosceles right triangle.

with the legs equal to the radius of the circle.

Using Pythagorean Theorem :

`\begin{gathered} r^2+r^2=12^2 \\ 2r^2=144 \\ r^2=(144)/(2)=72 \\ r=√(72)=6√(2) \end{gathered}`

So we have now a radius of r = 6√2

The height is h = 17

LA stands for the Lateral Area which is the area of the cylinder without the bases.

The formula for LA is :

`LA=2\pi rh`

Using the formula :

`\begin{gathered} LA=2\pi(6√(2))(17) \\ LA=906.3 \end{gathered}`

Now we have LA = 906.3

SA stands for the Surface area which is the total area including the bases.

The formula is :

`SA=2\pi r^2+2\pi rh`

Using the formula :

`\begin{gathered} SA=2\pi(6√(2))^2+2\pi(6√(2))(17) \\ SA=1358.7 \end{gathered}`

So we have SA = 1358.7

Last is the Volume with the formula of :

`V=\pi r^2h`

Using the formula :

`\begin{gathered} V=\pi(6√(2))^2(17) \\ V=3845.3 \end{gathered}`