Question

Question 1

Answer 1

Answer:

The volume of cone A is twice the volume of cone B.

Step-by-step explanation:

The formula that is used to find the volume of a cone is given by :

$V=\dfrac{1}{3}\pi r^2 h$

Where

r is radius of cone and h is height

ATQ,

The radius of the base of cone A is twice as large as the radius of the base of cone B. The  height of cone B is twice the height of cone A.

$r_A=2r_B\ \text{and}\ h_B=2h_A$

or

$\dfrac{r_A}{r_B}={2}\ \text{and}\ \dfrac{h_A}{h_B}=\dfrac{1}{2}$

Taking ratios of their volume,

$\dfrac{V_A}{V_B}=\dfrac{1/3\pi r_A^2h_A}{1/3\pi r_B^2h_B}\\\\\dfrac{V_A}{V_B}=(\dfrac{r_A}{r_B})^2\times \dfrac{h_A}{h_B}$

So,

$\dfrac{V_A}{V_B}=(\dfrac{r_A}{r_B})^2\times \dfrac{h_A}{h_B}\\\\\dfrac{V_A}{V_B}=(2)^2\times \dfrac{1}{2}\\\\\dfrac{V_A}{V_B}=2\\\\V_A=2V_B$

The volume of cone A is twice the volume of cone B.