Question 5

Explanation

Given:

• Cone A: Radius ($R_1$) is equal to height ($h_1$), so $R_1 = h_1$.
• Cone B: Radius ($R_2$) is twice the height ($h_2$), so $R_2 = 2h_2$ or $h_2 = \frac{1}{2}R_2$.
• Equal volumetric rate means $V_A = V_B$ (Volume of cone A equals Volume of cone B).

Recall the cone volume formula $V = \frac{1}{3}\pi R^2 h$.

Simplify by cancelling $\frac{1}{3}\pi$ on both sides:

Substitute the height-radius relationship for each cone:

• Replace $h_1$ with $R_1$
• Replace $h_2$ with $\frac{1}{2}R_2$

We want to find the ratio $R_1 : R_2$:

Take the cube root of both sides:

Thus, the ratio $R_1 : R_2 = 1 : \sqrt[3]{2}$.