Respuesta :
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 :
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
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.
[tex]r_A=2r_B\ \text{and}\ h_B=2h_A[/tex]
or
[tex]\dfrac{r_A}{r_B}={2}\ \text{and}\ \dfrac{h_A}{h_B}=\dfrac{1}{2}[/tex]
Taking ratios of their volume,
[tex]\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}[/tex]
So,
[tex]\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[/tex]
The volume of cone A is twice the volume of cone B.
