Create a cylinder with a height of 16 cm and a radius of 5 cm. What can be concluded about the cylinder’s volume when the height is halved? The volume is One-fourthof the original. The volume is One-thirdof the original. The volume is One-halfof the original. The volume is twice the original.

New volume is one-half of the original

Step-by-step explanation:

Step 1:

Find the original volume of the cylinder. Radius = 5 cm and height = 16 cm

Volume = πr²h = π × 5² × 16 = 400π

Step 2:

Find the volume when height is halved.

New volume = π × 5² × 8 = 200π

∴ New volume is one-half of the original.

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.