the radius of a cylinder Is 3.5 ft. The height is 14ft. Find the surface area and volume of the cylinder to the nearest foot show your work

Question

the radius of a cylinder Is 3.5 ft.  The height is 14ft.  Find the surface area and volume of the cylinder to the nearest foot show your work

campbell_st · Answer

Well the formula for volume is 

$$V = \pi r^2 h$$

surface area 

$$SA = 2\pi r^2h + 2\pi r h$$

this is provided the cylinder is closed. 

just substitute r = 3.5 and h = 14 to get your answers

goldphenoix · Answer

To find the volume of a cylinder, you must use area of the base times the height.
The radius of the cylinder is 3.5 ft. To find the area of the base (circle) you must do: $$\large\large r^2 \pi$$ Since the radius is 3.5. You do 3.5 square. 3.5 square is equal to $$\large12.25 \pi ft^2$$. The height is 14. Since we have the area of the base, and the height, you can find the volume. 12.25 x 14 is equal to 171.5 cubic feet. Don't forget to times pi. 171.5 times pi is equal to 538.73 cubic feet. So: $$\large V = 538.78 ft^3$$

To find the surface area, you must add up the 2 circle and the rectangle. Since we know that the area of the  circle is 12.25 pi. You can do 12.25 pi times 2 to get the area of the 2 circle. 
Now you want to find the area of the rectangle. We know that the height is 14. We need to find the other side of the rectange. To do this, we must find the circumference of the circle. To find the circumference of the circle, we must do 2r pi. The radius is 3.5. Multiplying it by 2 will give you 7. So the circumference of the circle is 7 pi. It is also the missing side of the rectangle. To find the total area of the rectangle you do 15 x 7 pi. This will give you 105 pi. 
The final step to finding the surface area of the cylinder is to add 105 pi, 12.25 pi, and 12.25 pi. This will give you 406.84 square feet. So: $$\large \large S.A = 406.84$$

goldphenoix · Answer

Wait, I mest up with the surface area.

anonymous · Answer

k @GoldPhenoix

goldphenoix · Answer

You can use the formula that the other person has given. So all you have to do is to plug the number in the formula. $$\large SA = 2 \pi r^2 h + 2 \pi r h$$ After plugging in the number, your equation should look like: $$\large \large SA = (2 \pi 3.5^2\times14) + (2 \pi 3.5 \times 14)$$

goldphenoix · Answer

I think I mest up again, let me check one more time.

goldphenoix · Answer

The surface area should be 384.845 square feet.

anonymous · Answer

okay thank you so much for your help