Question

V = 1/3 π r^2h; If V = 48 π when r = 4, find h

Answer 1

The height h of a cylinder with a given volume of 48 π and a radius of 4 is 9 units. This is determined using the formula V = 1/3 π r² h and solving for h.

Step-by-step explanation:

To find the height h of a cylinder when the volume V is given as 48 π and the radius r equals 4, we use the formula for the volume of a cylinder, V = ⅓ π r² h. We know that V = 48 π and r = 4. Plugging the values into the formula:

V = ⅓ π r² h

48 π = ⅓ π (4)² h

To isolate h, we first calculate r², which is 4² = 16. Then we can multiply both sides of the equation by 3 to get rid of the fraction and divide both sides by π, which gets canceled out:

144 = 16 h
h = 144 / 16
h = 9

So, the height h of the cylinder is 9 units.

Answer 2

`48\pi = (1)/(3) \pi {4}^(2) * h \\ we \: omit \: \pi \: each \: sides \\ \\ 48 = (16)/(3) * h \\ h = (3 * 48)/(16) = 3 * 3 = 9`