Question

The volume of the cone shown is 6 cubic inches. What is the height of a cone with the same base diameter but a volume of only 3 cubic inches? Please tell me the exact answer.

Answer 1

Answer:

3 cubic inches

Step-by-step explanation:

$volume \: of \: cone = \frac{1}{3} (base \: area)(height)$

Volume of cone shown= 6 cubic inches

Let the base diameter be 2x.

Therefore, radius= x

$\frac{1}{3} (\pi {x}^{2})(6) = 6 \\ \frac{1}{3} \pi {x}^{2} = 1 \: \: \: \: \: ( \div 6 \: throughout)$

Since the base diameter is the same, the base area is the same.

Using the formula, volume of cone$= \frac{1}{3} (\pi {x}^{2}) (3)$

Subst. the known value of $\frac{1}{3} \pi {x}^{2}$ into the equation.

Thus, volume of cone= 1(3)= 3 cubic inches