Question

Hello can you please help me determine the volume and surface area

Answer 1

The volume is 502.62 cubic inches

The surface area is 351.86 square inches.

To find the volume we use the formula for the volume of a cillinder:

`V=\pi r^2h`

Where r is the radius and h is the height. In this case:

`V=\pi\cdot4^2\cdot10=502.85in^3`

Now to find the surface area, we calculate the area of the circle on top and bottom of the cillinder (they are both equal to each other) and add the surface area of the sides.

We find this area by multipliying the height of the cillinder times the lenght of the circunference.

Let's calculate first the area of the circle:

`\text{Area circle= r}^2\pi=4^2\pi=50.265`

We have a circle on top and bottom of the cillinder, then we multiply by 2: 50.265*2=100.53 square inches.

Now calculate the circunference:

`2\pi r=2\pi4=8\pi\approx25.13`

Now we multiply the circunferrence times the height:

25.13*10=251.32 square inches.

Adding all up: 251.32+100.53=351.85 square inches