NIMCET 2026 — Reasoning PYQ

To find the ratio of the volumes, we utilize the standard geometric volume formulas for each shape. Let $r$ be the radius and $h$ be the height of the objects. Because the objects have the same radius and height, we define $h=r$ for these calculations.

Step 1: Define Volume Formulas

• Volume of the Cylinder ($V_{cyl}$):

  $$V_{cyl}=\pi r^{2}h=\pi r^2(r)=\pi r^3$$

• Volume of the Cone ($V_{cone}$):

  $$V_{cone}=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^2(r)=\frac{1}{3}\pi r^3$$

• Volume of the Hemisphere ($V_{hemi}$):

  $$V_{hemi}=\frac{2}{3}\pi r^3$$

Step 2: Calculate the Ratio

We need the ratio of Cylinder : Cone : Hemisphere:

$$\text{Ratio}=V_{cyl}:V_{cone}:V_{hemi}$$

Substituting the formulas:

$$\text{Ratio}=\pi r^3:\frac{1}{3}\pi r^3:\frac{2}{3}\pi r^3$$

By dividing each term by $\frac{1}{3}\pi r^3$, we simplify the ratio:

$$\text{Ratio}=3:1:2$$

Correct Answer:

The ratio of the volumes of the cylinder, cone, and hemisphere is 3:1:2, which corresponds to option 2.