Question

The formula for the volume, (V), of a cone having the radius, (r), and the height, (h), is shown below.

[ V = 1/3 π r² h ]

Write the formula to calculate the height, (h).
a) (h = 3V/π r²
b) (h = V/π r²
c) (h = π r²/3V
d) (h = π r²/V

Answer 1

To find the height of a cone when given its volume, the formula is rearranged to h = 3V/π r², which is option a).

Step-by-step explanation:

The student is asked to rearrange the formula for the volume of a cone to solve for the height (h). Given the formula V = 1/3 π r² h, we can isolate h by multiplying both sides of the equation by 3 and then dividing by π r²:

V = 1/3 π r² h

3V = π r² h

h = 3V / (π r²)

Therefore, the correct formula to calculate the height (h) of the cone is a) h = 3V/π r².