Question

Cone a and cone b both have a height of 5 in. The volume of cone a is 20.9cubic in, the volume of cone b is 4 times the volume of cone a, about how many times longwr is the diameter of cone b than the diameter of cone a?

Answer 1

Answer: two times

Step-by-step explanation:

Given

height of cone A and B  $h_a=h_b=5\ in.$

The volume of cone A  $V_a=20.9\ in.^3$

The volume of cone B is 4 times of cone A

the volume of a cone is  $\frac{1}{3}\pi r^2h$

The volume of cone A

$V_a=\dfrac{1}{3}\pi r_a^2h_a=20.9\quad \ldots(i)$

The volume of cone B

$V_b=\dfrac{1}{3}\pi r_b^2h_b=4\times 20.9\quad \ldots(ii)$

divide (i) and (ii) we get

$\Rightarrow \dfrac{r_a^2}{r_b^2}=\dfrac{1}{4}\\\Rightarrow \dfrac{r_a}{r_b}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}\\\Rightarrow \dfrac{d_a}{d_b}=\dfrac{1}{2}\\\Rightarrow d_b=2d_a$

thus, diameter of cone B is twice the diameter of A