Question 1

A square pyramid has a base side length of 8 cm and a height of 6 cm. What is the volume of the pyramid?

Accepted Answer

Step 1: Volume of a pyramid = (1/3) × base area × height. Step 2: Base area of square = 8² = 64 cm². Step 3: Height = 6 cm. Step 4: Volume = (1/3) × 64 × 6 = (1/3) × 384 = 128 cm³. Therefore, the answer is 128 cm³.

Question 2

A triangular prism has a triangular base with sides 3 cm, 4 cm, and 5 cm. The height of the prism is 10 cm. What is the lateral surface area of the prism?

Accepted Answer

Step 1: Identify that lateral surface area of a prism = perimeter of base × height of prism. Step 2: Perimeter of triangular base = 3 + 4 + 5 = 12 cm. Step 3: Lateral surface area = 12 × 10 = 120 cm². Therefore, the answer is 120 cm².

Question 3

A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. What is the total surface area of the prism?

Accepted Answer

Step 1: Total surface area of a rectangular prism = 2(lw + lh + wh). Step 2: Substitute l = 8, w = 6, h = 4. Step 3: TSA = 2(8×6 + 8×4 + 6×4) = 2(48 + 32 + 24) = 2(104) = 208 cm². Therefore, the answer is 208 cm².

Question 4

A triangular pyramid (tetrahedron) has a triangular base with area 24 cm² and a height of 9 cm. What is the volume of the pyramid?

Accepted Answer

Step 1: Volume of a pyramid = (1/3) × base area × height. Step 2: Substitute base area = 24 cm² and height = 9 cm. Step 3: Volume = (1/3) × 24 × 9 = (1/3) × 216 = 72 cm³. Therefore, the answer is 72 cm³.

Question 5

A pentagonal prism has a regular pentagonal base with perimeter 50 cm. The height of the prism is 12 cm. What is the lateral surface area of the prism?

Accepted Answer

Step 1: Lateral surface area of a prism = perimeter of base × height. Step 2: Perimeter of pentagonal base = 50 cm. Step 3: Height of prism = 12 cm. Step 4: LSA = 50 × 12 = 600 cm². Therefore, the answer is 600 cm².

Question 6

A rectangular prism has dimensions 5 cm × 8 cm × 10 cm. If a smaller rectangular prism with dimensions 2 cm × 4 cm × 5 cm is removed from it, what is the ratio of the remaining volume to the original volume?

Accepted Answer

Step 1: Original volume = 5 × 8 × 10 = 400 cm³. Step 2: Removed volume = 2 × 4 × 5 = 40 cm³. Step 3: Remaining volume = 400 − 40 = 360 cm³. Step 4: Ratio = 360 : 400 = 9 : 10.

Question 7

A pentagonal prism has a regular pentagonal base with side 4 cm. The perimeter of the base is 20 cm. If the height of the prism is 12 cm, what is the lateral surface area in cm²?

Accepted Answer

Step 1: The lateral surface area of any prism = perimeter of base × height. Step 2: Perimeter of pentagonal base = 5 × 4 = 20 cm (confirmed in question). Step 3: Lateral surface area = 20 × 12 = 240 cm².

Question 8

A hexagonal prism has a regular hexagonal base with side 3 cm. The height of the prism is 8 cm. What is the volume of the prism in cm³? (Use: area of regular hexagon = (3√3/2) × side²)

Accepted Answer

Step 1: Area of regular hexagonal base = (3√3/2) × side² = (3√3/2) × 9 = (27√3/2) cm². Step 2: Using √3 ≈ 1.732, area ≈ 23.38 cm². Step 3: Volume = base area × height = 23.38 × 8 ≈ 187 cm³. (Exact: 108√3 cm³ ≈ 187.06 cm³). For multiple choice, the closest integer is 187 cm³.

Question 9

A triangular prism has an equilateral triangular base with side 6 cm. The prism's length is 12 cm. What is the lateral surface area (excluding the two triangular bases) in cm²?

Accepted Answer

Step 1: The lateral surface area of a prism consists of 3 rectangular faces. Step 2: Each rectangular face has dimensions: side of triangle (6 cm) × length of prism (12 cm). Step 3: Area of one rectangular face = 6 × 12 = 72 cm². Step 4: Total lateral surface area = 3 × 72 = 216 cm².

Question 10

A square pyramid has a base side of 8 cm. The perpendicular height from the apex to the base is 6 cm. What is the volume of the pyramid in cm³?

Accepted Answer

Step 1: Area of square base = 8² = 64 cm². Step 2: Perpendicular height of pyramid = 6 cm. Step 3: Volume of pyramid = (1/3) × Base area × Height = (1/3) × 64 × 6 = (1/3) × 384 = 128 cm³.

IBPS RRB PO Prism & Pyramid

Prism & Pyramid— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Prism & Pyramid — Practice Questions

60-Second Revision — Prism & Pyramid