What is the volume of a cylinder, in cubic feet, with a height of 8 feet and a base diameter of 18 feet? Round to the nearest tenths place

2034.7 ft³

Step-by-step explanation:

To calculate the volume of a cylinder, use the formula V = bh.

The base of a cylinder is a circle, therefore you must solve for the area of a circle using the formula A = πr²

Since the diameter is given as 18, half of that is the radius, or 9. Plug this into the formula for the area of the base:

A = 9²π

A = 81π ≈ 254.34

That is the area of the base. Plug that into the equation for the volume of a cylinder:

V = (254.34) · 8

V = 2034.72 ≅ 2034.7 ft³ (Rounded to tenths)

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

what is the answer?