Which of the following statements are incorrect? (a) Volume of a cone = 1/3 r^3 h (b) Volume of a cone = 1/3 r^2 h (c) Volume of a hemisphere = 2/3 r^2 (d) Volume of a hemisphere = 2/3 r^3 (e) Volume of a cylinder = 1/3 r^3 h Choose the correct answer from the options given below: Option 1: (a), (b) and (d) only Option 2: (a), (b) and (c) only Option 3: (a), (c) and (e) only Option 4: (c), (d) and (e) only

Answer: (a), (c) and (e) only. Solution: The standard formulas are: volume of cone = 1/3 r^2 h, volume of hemisphere = 2/3 r^3, volume of cylinder = r^2 h. Therefore statements (a), (c) and (e) are incorrect, while (b) and (d) are correct.

Geometry

Solids

Easy

Which of the following statements are incorrect?

(a) Volume of a cone = $\frac{1}{3}\pi r^3 h$

(b) Volume of a cone = $\frac{1}{3}\pi r^2 h$

(c) Volume of a hemisphere = $\frac{2}{3}\pi r^2$

(d) Volume of a hemisphere = $\frac{2}{3}\pi r^3$

(e) Volume of a cylinder = $\frac{1}{3}\pi r^3 h$

Choose the correct answer from the options given below:

(a), (b) and (d) only

(a), (b) and (c) only

(a), (c) and (e) only

(c), (d) and (e) only

✅ Correct Option: 3

The standard formulas are: volume of cone = $\frac{1}{3}\pi r^2 h$ , volume of hemisphere = $\frac{2}{3}\pi r^3$ , volume of cylinder = $\pi r^2 h$ . Therefore statements (a), (c) and (e) are incorrect, while (b) and (d) are correct.

2026: 29 May Shift 2

Find the total surface area of a solid hemisphere of diameter 14 cm.

2025: 24 May Shift 2

If the areas of adjacent faces of a cuboid (rectangular prism) are in the ratio of 2: 3: 5 and its volume is 900 cm³, then the length of the longest side is

2026: 24 May Shift 1

The radius of cylinder is 7 cm and height is 11 cm. The total surface area of cylinder will be:

2025: 15 May Shift 1

Match List-I with List-II

List-I	List-II
(Figures, etc.)	(Area/Volume/Diagonal etc.)
(A) Surface area of Cube	(I) $\pi(R^2 - r^2)$
(B) Volume of Right pyramid	(II) $a\sqrt{2}$
(C) Area of Circular Ring	(III) $6a^2$
(D) Diagonal of Square	(IV) $\frac{1}{3}$ (area of base) × height

Choose the correct answer from the options given below:

2023: 15 June Shift 2

The surface area (in $m^2$ ) of a sphere of radius 7 cm is:

Use $\pi = \frac{22}{7}$

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:

Solution

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