Question 1

A rectangular prism has a square base with side length 6 cm and a height of 10 cm. What is the total surface area of the prism?

Accepted Answer

Step 1: Identify the dimensions — square base with side = 6 cm, height = 10 cm. Step 2: Surface area of a rectangular prism = 2(base area) + (perimeter of base × height). Step 3: Base area = 6 × 6 = 36 cm². Step 4: Perimeter of base = 4 × 6 = 24 cm. Step 5: Lateral surface area = 24 × 10 = 240 cm². Step 6: Total surface area = 2(36) + 240 = 72 + 240 = 312 cm². Therefore, the answer is 312 cm².

Question 2

A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. What is the total surface area of the prism?

Accepted Answer

Step 1: Identify the dimensions: length (l) = 12 cm, width (w) = 8 cm, height (h) = 5 cm. Step 2: Apply the surface area formula for a rectangular prism: SA = 2(lw + wh + lh). Step 3: Calculate each face area: lw = 12 × 8 = 96, wh = 8 × 5 = 40, lh = 12 × 5 = 60. Step 4: Sum the face areas: 96 + 40 + 60 = 196. Step 5: Multiply by 2: SA = 2 × 196 = 392 cm². Therefore, the answer is 392 cm².

Question 3

A triangular prism has a triangular base with area 24 cm² and height (length) of the prism is 10 cm. What is the volume of the prism?

Accepted Answer

Step 1: Identify the formula for volume of a prism: V = Base Area × Height. Step 2: Substitute values: V = 24 × 10 = 240 cm³. Therefore, the answer is 240 cm³.

Question 4

A triangular pyramid (tetrahedron) has a triangular base with area 36 cm² and height 9 cm. Find its volume.

Accepted Answer

Step 1: Use the pyramid volume formula: Volume = (1/3) × Base Area × Height. Step 2: Substitute the values: Volume = (1/3) × 36 × 9 = (1/3) × 324 = 108 cm³. Therefore, the answer is 108 cm³.

Question 5

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 6

A rectangular prism has dimensions 5 cm × 6 cm × 10 cm. What is its volume?

Accepted Answer

Step 1: Apply the volume formula for a rectangular prism: Volume = length × width × height. Step 2: Substitute values: Volume = 5 × 6 × 10 = 300 cm³. Therefore, the answer is 300 cm³.

Question 7

A pentagonal prism has a pentagonal base with area 50 cm² and the prism's height is 8 cm. What is the volume?

Accepted Answer

Step 1: Apply the prism volume formula: Volume = Base Area × Height. Step 2: The shape of the base (pentagon) doesn't change the formula; we use the given area directly. Volume = 50 × 8 = 400 cm³. Therefore, the answer is 400 cm³.

Question 8

A hexagonal pyramid has a hexagonal base with area 54 cm² and height 10 cm. What is the volume of the pyramid?

Accepted Answer

Step 1: Apply pyramid volume formula: V = (1/3) × Base Area × Height. Step 2: V = (1/3) × 54 × 10 = (1/3) × 540 = 180 cm³. Therefore, the answer is 180 cm³.

Question 9

A pentagonal prism has a pentagonal base with area 40 cm² and the prism's length is 7 cm. What is the volume of the prism?

Accepted Answer

Step 1: Apply prism volume formula: V = Base Area × Length. Step 2: V = 40 × 7 = 280 cm³. Therefore, the answer is 280 cm³.

Question 10

A triangular pyramid (tetrahedron) has a triangular base with area 15 cm² and height 12 cm. What is its volume?

Accepted Answer

Step 1: Apply pyramid volume formula: V = (1/3) × Base Area × Height. Step 2: V = (1/3) × 15 × 12 = (1/3) × 180 = 60 cm³. Therefore, the answer is 60 cm³.

Question 11

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

Accepted Answer

Step 1: Volume of a pyramid = ⅓ × base area × height. Step 2: Volume = ⅓ × 24 × 9 = ⅓ × 216 = 72 cm³. Therefore, the answer is 72 cm³.

Question 12

A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. What is the total surface area of the prism?

Accepted Answer

Step 1: Identify the formula for surface area of a rectangular prism: SA = 2(lw + lh + wh). Step 2: Substitute values: SA = 2(12×8 + 12×5 + 8×5) = 2(96 + 60 + 40) = 2(196) = 392 cm². Therefore, the answer is 392 cm².

Question 13

A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. What is its volume?

Accepted Answer

Step 1: Volume of a rectangular prism = length × width × height. Step 2: Volume = 8 × 6 × 4 = 192 cm³. Therefore, the answer is 192 cm³.

Question 14

A rectangular prism has dimensions 6 cm × 4 cm × 5 cm. What is its total surface area?

Accepted Answer

Step 1: Total surface area of a rectangular prism = 2(lw + lh + wh). Step 2: Substitute l = 6, w = 4, h = 5. Step 3: TSA = 2(6×4 + 6×5 + 4×5) = 2(24 + 30 + 20) = 2(74) = 148 cm². Therefore, the answer is 148 cm².

Question 15

A hexagonal pyramid has a regular hexagonal base with area 72 cm² and height 10 cm. Calculate its volume.

Accepted Answer

Step 1: Use the pyramid volume formula: Volume = (1/3) × Base Area × Height. Step 2: Substitute values: Volume = (1/3) × 72 × 10 = (1/3) × 720 = 240 cm³. Therefore, the answer is 240 cm³.

Question 16

A square pyramid has a base side length of 8 cm and height 12 cm. What is the volume of the pyramid?

Accepted Answer

Step 1: Calculate the base area of the square: Base Area = 8² = 64 cm². Step 2: Apply pyramid volume formula: Volume = (1/3) × Base Area × Height = (1/3) × 64 × 12 = (1/3) × 768 = 256 cm³. Therefore, the answer is 256 cm³.

Question 17

A triangular prism has a triangular base with area 24 cm² and height 15 cm. What is the volume of the prism?

Accepted Answer

Step 1: Identify the formula for volume of a prism: Volume = Base Area × Height. Step 2: Substitute values: Volume = 24 × 15 = 360 cm³. Therefore, the answer is 360 cm³.

Question 18

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 19

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

Accepted Answer

Step 1: Calculate base area of square: A = 6² = 36 cm². Step 2: Apply pyramid volume formula: V = (1/3) × Base Area × Height. Step 3: V = (1/3) × 36 × 8 = (1/3) × 288 = 96 cm³. Therefore, the answer is 96 cm³.

Question 20

A triangular prism has an equilateral triangular base with side 10 cm and prism height 15 cm. What is the lateral surface area of the prism?

Accepted Answer

Step 1: Lateral surface area of a prism = perimeter of base × height of prism. Step 2: Perimeter of equilateral triangle = 3 × 10 = 30 cm. Step 3: Lateral surface area = 30 × 15 = 450 cm².

Question 21

A rectangular prism has dimensions 5 cm × 8 cm × 10 cm. If the volume is to remain constant, and the length is increased to 16 cm, what should be the new product of width and height?

Accepted Answer

Step 1: Original volume = 5 × 8 × 10 = 400 cm³. Step 2: New volume must equal 400 cm³. Step 3: With new length = 16 cm, we have 16 × (width × height) = 400. Step 4: width × height = 400 ÷ 16 = 25 cm².

Question 22

A triangular pyramid (tetrahedron) has an equilateral triangular base with side 6 cm and a height of 4 cm. What is the volume of the pyramid in cm³? (Use √3 ≈ 1.73)

Accepted Answer

Step 1: Area of equilateral triangle base = (√3/4) × side² = (√3/4) × 6² = (√3/4) × 36 = 9√3 cm². Step 2: Using √3 ≈ 1.73, area ≈ 9 × 1.73 = 15.57 cm². Step 3: Volume of pyramid = (1/3) × base area × height = (1/3) × 15.57 × 4 ≈ (1/3) × 62.28 ≈ 20.76 cm³. Rounding to nearest integer: 21 cm³. (Exact: 12√3 ≈ 20.76 cm³)

CDS Prism & Pyramid

CDS Prism & Pyramid — Past Exam Questions

Prism & Pyramid — Practice Questions