Question

DRILLING The volume of a drill bit can be estimated by the formula for a cone, V=13πhr2,

where h is the height of the bit and r is its radius. Substituting 3√3r
for h, the volume of the drill bit can be estimated by V=3√9πr3.



What is the volume of a drill bit with a radius of 3 centimeters? Complete the following with an exact expression: __ cm3

Answer 1

The exact volume of a drill bit with a radius of 3 cm is calculated using the formula V=3√9πr^3, resulting in an exact expression of 27π cm^3.

Step-by-step explanation:

The volume of a drill bit with a radius of 3 centimeters can be calculated using the given formula V=3√9πr3. To find the exact expression for the volume:

1. Substitute the radius (r) with 3 cm into the formula, which gives us V=3√9π(3 cm)3.
2. First, calculate (3 cm)3 = 27 cm3.
3. Next, multiply this by 9 to get 9 × 27 cm3 = 243 cm3.
4. Then, calculate the cubic root of 243, which is 3√243 = 3 √(35) = 32 = 9.
5. Finally, multiply this by π to get the volume V = 3 × 9 × π cm3 = 27π cm3.

Thus, the exact volume of the drill bit with a radius of 3 cm is 27π cm3.