If r represent the radius and h denotes the height of the solid. Then, Match List-I with List-II, LIST-I (Solid), LIST-II (Volume), A. Cylinder, I. 2/3 r^3, B. Cone, II. 4/3 r^3, C. Sphere, III. 1/3 r^2 h, D. Hemisphere, IV. r^2 h, Choose the correct answer from the options given below: Option 1: A-I, B-II, C-III, D-IV Option 2: A-IV, B-II, C-III, D-I Option 3: A-IV, B-III, C-II, D-I Option 4: A-III, B-IV, C-II, D-I

Answer: A-IV, B-III, C-II, D-I. Solution: Cylinder = r^2 h (IV), cone = 1/3 r^2 h (III), sphere = 4/3 r^3 (II) and hemisphere = 2/3 r^3 (I). Hence A-IV, B-III, C-II, D-I.

Geometry

Solids

Easy

If r represent the radius and h denotes the height of the solid. Then, Match List-I with List-II

LIST-I (Solid) LIST-II (Volume)
A. Cylinder I. $\dfrac{2}{3}\pi r^3$
B. Cone II. $\dfrac{4}{3}\pi r^3$
C. Sphere III. $\dfrac{1}{3}\pi r^2 h$
D. Hemisphere IV. $\pi r^2 h$

Choose the correct answer from the options given below:

LIST-I (Solid)	LIST-II (Volume)
A. Cylinder	I. $\dfrac{2}{3}\pi r^3$
B. Cone	II. $\dfrac{4}{3}\pi r^3$
C. Sphere	III. $\dfrac{1}{3}\pi r^2 h$
D. Hemisphere	IV. $\pi r^2 h$

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

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

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

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

✅ Correct Option: 3

Cylinder $= \pi r^2 h$ (IV), cone $= \dfrac{1}{3}\pi r^2 h$ (III), sphere $= \dfrac{4}{3}\pi r^3$ (II) and hemisphere $= \dfrac{2}{3}\pi r^3$ (I). Hence A-IV, B-III, C-II, D-I.

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If the radius of a sphere is increased by 50%, find the percent increase in surface area.

2025: 3 June Shift 1

The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced 25 %, then its total surface area is reduced to 318.5π m². What is the circumference of the base of the cylinder?

2026: 18 May Shift 1

A rectangular sheet 50 cm by 30 cm is rolled along the 30 cm side to form a cylinder (open at both ends). The radius of the cylinder is:

2026: 26 May Shift 1

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between the surface areas (in cm²) of two solids.

2023: 1 June Shift 1

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2025: 26 May Shift 1

A right circular metal cone (solid) is 42 cm high and its radius is $\frac{21}{2}$ cm. It is melted and recast into a sphere. Then the radius of the sphere will be:

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