Question 1

A square prism (cuboid with square base) has base side 6 cm and height 10 cm. Find its lateral surface area.

Accepted Answer

Step 1: Lateral surface area of prism = perimeter of base × height. Step 2: Perimeter of square base = 4 × 6 = 24 cm. Step 3: Lateral surface area = 24 × 10 = 240 cm². Therefore, the answer is 240 cm².

Question 2

A pyramid with rectangular base has length 8 cm, width 6 cm, and height 12 cm. What is its volume?

Accepted Answer

Step 1: Base area = length × width = 8 × 6 = 48 cm². Step 2: Volume of pyramid = (1/3) × base area × height = (1/3) × 48 × 12 = (1/3) × 576 = 192 cm³. Therefore, the answer is 192 cm³.

Question 3

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

Accepted Answer

Step 1: Surface area of rectangular prism = 2(lw + lh + wh). Step 2: = 2(12×8 + 12×5 + 8×5) = 2(96 + 60 + 40) = 2(196) = 392 cm². Therefore, the answer is 392 cm².

Question 4

A triangular pyramid has a base area of 24 cm² and height 9 cm. What is its volume?

Accepted Answer

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

Question 5

A pyramid with a rectangular base of dimensions 8 m × 6 m has a height of 12 m. What is the volume of the pyramid?

Accepted Answer

Step 1: Volume of a pyramid = (1/3) × Base Area × Height. Step 2: Base Area = 8 × 6 = 48 m². Step 3: Volume = (1/3) × 48 × 12 = (1/3) × 576 = 192 m³. Therefore, the answer is 192 m³.

Question 6

A right circular cone has a base radius of 7 cm and a slant height of 25 cm. What is the curved surface area of the cone?

Accepted Answer

Step 1: Curved Surface Area of a cone = π × r × l, where r is radius and l is slant height. Step 2: CSA = π × 7 × 25 = 175π cm². Step 3: Using π ≈ 22/7, CSA = 175 × (22/7) = 25 × 22 = 550 cm². Therefore, the answer is 550 cm².

Question 7

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 8

A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. A pyramid with the same rectangular base (8 cm × 6 cm) and height 12 cm is placed on top of the prism. What is the total volume of the combined solid in cm³?

Accepted Answer

Step 1: Volume of rectangular prism = length × width × height = 8 × 6 × 4 = 192 cm³. Step 2: Volume of pyramid = (1/3) × base area × height = (1/3) × (8 × 6) × 12 = (1/3) × 48 × 12 = (1/3) × 576 = 192 cm³. Step 3: Total volume = 192 + 192 = 384 cm³.

Question 9

A hexagonal prism has a regular hexagonal base with side length 5 cm and prism height 15 cm. What is the lateral surface area of the prism in cm²?

Accepted Answer

Step 1: A regular hexagon has 6 equal sides. Perimeter of hexagonal base = 6 × 5 = 30 cm. Step 2: Lateral surface area of a prism = perimeter of base × height of prism = 30 × 15 = 450 cm².

Question 10

A right triangular prism has a triangular base with sides 13 cm, 14 cm, and 15 cm. The height of the prism is 20 cm. What is the total surface area of the prism in cm²?

Accepted Answer

Step 1: Find the area of the triangular base using Heron's formula. Semi-perimeter s = (13+14+15)/2 = 21 cm. Area = √[21(21-13)(21-14)(21-15)] = √[21×8×7×6] = √7056 = 84 cm². Step 2: Find the perimeter of the base = 13+14+15 = 42 cm. Step 3: Lateral surface area = perimeter × height = 42 × 20 = 840 cm². Step 4: Total surface area = 2 × base area + lateral surface area = 2(84) + 840 = 168 + 840 = 1008 cm².

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60-Second Revision — Prism & Pyramid