In the given figure, the radius of the cone is same as its height equal to 2 cm each. The sum of the volumes of the whole body is :

(i) 16π cm³

(ii) 16 cm³

(iii) 32π cm³

(iv) 32 cm³

To solve this problem, we need to calculate the volume of the cone described in the figure. The radius \( r \) and height \( h \) of the cone are both given as 2 cm.

### Volume of the cone:
The formula for the volume of a cone is:
\[
V = \frac{1}{3} \pi r^2 h
\]

Substitute the values:
\[
V = \frac{1}{3} \pi (2)^2 (2) = \frac{1}{3} \pi (4)(2) = \frac{1}{3} \pi (8) = \frac{8\pi}{3} \, \text{cm}^3
\]

Now, it seems that this problem involves the sum of volumes, but only one cone is mentioned. If there is additional information about other shapes in the "whole body" of the figure that you have (such as a cylinder or hemisphere), please provide more details.

Among the options, the total volume does not match the given choices. Could you clarify or upload the figure for more context? This would allow us to properly determine the sum of volumes.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How do you calculate the surface area of the same cone?
2. What is the lateral surface area of a cone with height and radius equal?
3. What changes if the cone height is doubled while keeping the radius the same?
4. How does the volume formula differ for a cylinder versus a cone?
5. How would the volume change if the radius and height are doubled?

**Tip:** Always confirm the dimensions and types of shapes involved when calculating volume in composite figures.

In the given figure, the radius of the cone is same as its height equal to 2 cm each. The sum of the volumes of the whole body is: (i) 16π cm³ (ii) 16 cm³ (iii) 32π cm³ (iv) 32 cm³

Learn how to calculate the volume of a cone where the radius and height are both 2 cm. This detailed solution uses the volume of a cone formula, solving for the total volume of the body in question. Suitable for students in Grades 8-10.

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