Question

Match List I with List II

List-I		List-II
(A)	Volume of cone	(I)	\(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\)
(B)	Volume of sphere	(II)	\(\frac{1}{3}\pi r^2h\)
(C)	Volume of Frustum	(III)	\(\pi r^2h\)
(D)	Volume of cylinder	(IV)	\(\frac{4}{3}\pi r^3\)

Choose the correct answer from the options given below:

• A. A-IV, B-I, C-III, D-II
• B. A-III, B-IV, C-II, D-I
• C. A-I, B-II, C-III, D-IV
• D. A-II, B-IV, C-I, D-III

Answer 1

The Correct Option is D

To solve the problem, we need to match the formulas for the volumes with their respective 3D solids from List-I and List-II.

List-I contains:

• (A) Volume of cone
• (B) Volume of sphere
• (C) Volume of Frustum
• (D) Volume of cylinder

List-II contains:

• (I) \(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\)
• (II) \(\frac{1}{3}\pi r^2h\)
• (III) \(\pi r^2h\)
• (IV) \(\frac{4}{3}\pi r^3\)

Let's match them:

1. Volume of a Cone (A): The formula for the volume of a cone is \(\frac{1}{3}\pi r^2h\). This corresponds to option (II).
2. Volume of a Sphere (B): The formula for the volume of a sphere is \(\frac{4}{3}\pi r^3\). This corresponds to option (IV).
3. Volume of a Frustum (C): The formula for the volume of a frustum of a cone is \(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\). This corresponds to option (I).
4. Volume of a Cylinder (D): The formula for the volume of a cylinder is \(\pi r^2h\). This corresponds to option (III).

Therefore, the correct match is:

A-II, B-IV, C-I, D-III