Match the given areas of various solid objects with their respective formulae:, List I, List II, Area of solid object, Formula, (A) Lateral surface area of a cylinder, (I) r√(r^2 + h^2), (B) Total surface area of a hemisphere, (II) 4 r^2, (C) Lateral surface area of a cone, (III) 2 rh, (D) Surface area of a sphere, (IV) 3 r^2, (Where, r = radius of the solid shape (or base) and h = height of the solid shape.) Choose the correct answer from the options given below: Option 1: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) Option 2: (A) - (I), (B) - (II), (C) - (III), (D) - (IV) Option 3: (A) - (I), (B) - (IV), (C) - (III), (D) - (II) Option 4: (A) - (III), (B) - (II), (C) - (I), (D) - (IV)

Answer: (A) - (III), (B) - (IV), (C) - (I), (D) - (II). Solution: The lateral surface area of a cylinder is the curved surface, excluding the top and bottom circles. For a cylinder with radius r and height h: Lateral surface area = 2 rh Match: (A) → (III) A hemisphere is half of a sphere. The total surface area includes the curved dome and the flat circular base. Curved surface area = 2 r^2 Flat circular base = r^2 Total surface area = 2 r^2 + r^2 = 3 r^2 Match: (B) → (IV) The lateral surface area of a cone is the slanted curved surface, excluding the base. The slant height from the tip to the edge of the base = √(r^2 + h^2) Lateral surface area = r x slant height = r√(r^2 + h^2) Match: (C) → (I) The surface area of a sphere with radius r: Surface area = 4 r^2 Match: (D) → (II) Final matching: (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Geometry

Solids

Easy

Match the given areas of various solid objects with their respective formulae:

List I List II
Area of solid object Formula
(A) Lateral surface area of a cylinder (I) $\pi r\sqrt{r^2 + h^2}$
(B) Total surface area of a hemisphere (II) $4\pi r^2$
(C) Lateral surface area of a cone (III) $2\pi rh$
(D) Surface area of a sphere (IV) $3\pi r^2$

(Where, r = radius of the solid shape (or base) and h = height of the solid shape.)

Choose the correct answer from the options given below:

List I	List II
Area of solid object	Formula
(A) Lateral surface area of a cylinder	(I) $\pi r\sqrt{r^2 + h^2}$
(B) Total surface area of a hemisphere	(II) $4\pi r^2$
(C) Lateral surface area of a cone	(III) $2\pi rh$
(D) Surface area of a sphere	(IV) $3\pi r^2$

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

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

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

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

✅ Correct Option: 1

The lateral surface area of a cylinder is the curved surface, excluding the top and bottom circles.

For a cylinder with radius $r$ and height $h$ :

Lateral surface area $= 2\pi rh$

Match: (A) → (III)

A hemisphere is half of a sphere. The total surface area includes the curved dome and the flat circular base.

Curved surface area $= 2\pi r^2$

Flat circular base $= \pi r^2$

Total surface area $= 2\pi r^2 + \pi r^2$

$= 3\pi r^2$

Match: (B) → (IV)

The lateral surface area of a cone is the slanted curved surface, excluding the base.

The slant height from the tip to the edge of the base $= \sqrt{r^2 + h^2}$

Lateral surface area $= \pi r \times \text{slant height}$

$= \pi r\sqrt{r^2 + h^2}$

Match: (C) → (I)

The surface area of a sphere with radius $r$ :

Surface area $= 4\pi r^2$

Match: (D) → (II)

Final matching:

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

2026: 31 May Shift 2

A rectangular block with sides 6 cm, 12 cm and 15 cm is cut up into an exact number of equal cubes. The least possible number of cubes is?

2025: 20 May Shift 1

The base radius of a cone is 21 cm and the height is 28cm, then which of the following is/are correct?

(A) Slant height = 35 cm

(B) Slant height = 33 cm

(D) Curved Surface Area = 2310 cm²

Choose the correct answer from the options given below:

2025: 2 June Shift 2

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

2023: 24 May Shift 3

64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

2025: 13 May Shift 1

The base diameter of a cylinder is 21 cm and the height is 28 cm, then:

(A) Radius of cylinder = 10.5 cm

(B) Volume = 12936 cm³

(D) Total surface area = 2541 cm²

Which of the following is/ are correct?

Choose the correct answer from the options given below:

2026: 20 May Shift 2

A right circular cylinder has radius 7 cm and height 10 cm. Another cylinder has twice the height and half the radius. The ratio of their volumes (first : second) is:

Solution

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