The radius of the base and height of a cone are 5 cm and 6 cm, respectively, whereas the radius of the base and height of a cylinder are 2.5 cm and 3 cm, respectively. The ratio of the volume of the cone to that of the cylinder is:

(Where $\pi =\frac{22}{7}$ )

The correct answer is 8:3.

Step 1: Calculate the volume of the cone
Given:
Radius of the base of the cone (r₁) = 5 cm
Height of the cone (h₁) = 6 cm

The formula for the volume of a cone is:

$V_{\text{cone}}=\frac{1}{3}\pi r_1^2{h}_1$

Substituting the given values into the formula:

$V_{\text{cone}}=\frac{1}{3}\times \pi \times {\left(5\right)}^2\times 6$

$V_{\text{cone}}=\frac{1}{3}\times \pi \times 25\times 6$

$V_{\text{cone}}=50\pi$ cm³

Step 2: Calculate the volume of the cylinder
Given:
Radius of the base of the cylinder (r₂) = 2.5 cm
Height of the cylinder (h₂) = 3 cm

The formula for the volume of a cylinder is:

$V_{\text{cylinder}}=\pi r_2^2{h}_2$

Substituting the given values into the formula:

$V_{\text{cylinder}}=\pi \times {\left(2.5\right)}^2\times 3$

$V_{\text{cylinder}}=\pi \times 6.25\times 3$

$V_{\text{cylinder}}=18.75\pi$ cm³

Step 3: Find the ratio of the volume of the cone to that of the cylinder
The ratio is given by:

$\text{Ratio}=\frac{V_{\text{cone}}}{V_{\text{cylinder}}}$

$\text{Ratio}=\frac{50\pi }{18.75\pi }$

Canceling π from both numerator and denominator:

$\text{Ratio}=\frac{50}{18.75}$

Multiplying the numerator and denominator by 4 to remove the decimal:

$\text{Ratio}=\frac{50\times 4}{18.75\times 4}=\frac{200}{75}$

Simplifying the fraction by dividing numerator and denominator by 25:

$\text{Ratio}=\frac{8}{3}$

Thus, the ratio of the volume of the cone to that of the cylinder is 8:3.