Question 1

A triangle has a base of 12 cm and a height of 8 cm. What is its area?

Accepted Answer

Step 1: Use the formula for the area of a triangle: Area = (1/2) × base × height. Step 2: Substitute the values: Area = (1/2) × 12 × 8 = (1/2) × 96 = 48 cm². Therefore, the area is 48 cm².

Question 2

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 3

A solid sphere has a radius of 7 cm. What is the volume of the sphere? (Use π = 22/7)

Accepted Answer

Step 1: Recall the formula for volume of a sphere: V = (4/3)πr³. Step 2: Substitute r = 7 cm and π = 22/7. Step 3: V = (4/3) × (22/7) × 7³ = (4/3) × (22/7) × 343. Step 4: V = (4/3) × 22 × 49 = (4 × 22 × 49)/3 = 4312/3 ≈ 1437.33 cm³. Step 5: Simplifying: V = (4 × 22 × 343)/(3 × 7) = (4 × 22 × 49)/3 = 4312/3. Calculating: 4312 ÷ 3 = 1437⅓ cm³ or exactly 1437.33 cm³. However, for cleaner computation: (4/3) × (22/7) × 343 = (88 × 343)/21 = 30184/21 = 1437⅓ cm³. Rounding to standard form: approximately 1437.33 cm³, but the exact answer is 4312/3 cm³ or 1437⅓ cm³. For SSC purposes, this equals **1437.33 cm³** or **4312/3 cm³**. Let me recalculate cleanly: V = (4/3) × (22/7) × 343 = (4 × 22 × 343)/(3 × 7) = (4 × 22 × 49)/3 = 4312/3 cm³. In decimal: **1437.33 cm³** (approximately). Standard answer: **1437⅓ cm³** or **4312/3 cm³**. For multiple choice, this is typically presented as **1437.33 cm³** or rounded to **1437 cm³** or **1440 cm³**.

Question 4

A circular garden has a radius of 14 metres. What is the difference between its circumference and diameter?

Accepted Answer

Step 1: Calculate the circumference using the formula C = 2πr. With r = 14 m and π = 22/7, we get C = 2 × (22/7) × 14 = 2 × 22 × 2 = 88 metres. Step 2: Calculate the diameter using d = 2r = 2 × 14 = 28 metres. Step 3: Find the difference: 88 − 28 = 60 metres. Therefore, the answer is 60 metres.

Question 5

The radius of a circle is 7 cm. What is the area of the circle? (Use π = 22/7)

Accepted Answer

Step 1: Recall the formula — Area = π × r². Step 2: Substitute r = 7 cm and π = 22/7. Step 3: Area = (22/7) × 7 × 7 = (22/7) × 49 = 22 × 7 = 154 cm². Therefore, the area of the circle is 154 cm².

Question 6

A right-angled triangle has legs of length 6 cm and 8 cm. What is the length of its hypotenuse?

Accepted Answer

Step 1: Use the Pythagorean theorem: c² = a² + b², where c is the hypotenuse and a, b are the legs. Step 2: Substitute: c² = 6² + 8² = 36 + 64 = 100. Step 3: c = √100 = 10 cm. Therefore, the hypotenuse is 10 cm.

Question 7

Two lines intersect each other. If one of the angles formed at the intersection is 65°, what is the measure of its vertically opposite angle?

Accepted Answer

Step 1: Recall the Vertically Opposite Angles theorem — when two lines intersect, vertically opposite angles are always equal. Step 2: The angle vertically opposite to 65° is also 65°. Therefore, the answer is 65°.

Question 8

The base of a triangle is 14 cm and its height is 10 cm. What is the area of the triangle?

Accepted Answer

Step 1: Recall the formula for area of a triangle = (1/2) × base × height. Step 2: Substitute the values: Area = (1/2) × 14 × 10 = (1/2) × 140 = 70 cm². Therefore, the answer is 70 cm².

Question 9

A trapezium has parallel sides of 14 cm and 10 cm, and height 6 cm. Find its area.

Accepted Answer

Step 1: Recall the formula for area of a trapezium: A = (1/2) × (sum of parallel sides) × height. Step 2: Substitute the parallel sides as 14 cm and 10 cm, and height = 6 cm. Step 3: A = (1/2) × (14 + 10) × 6 = (1/2) × 24 × 6 = (1/2) × 144 = 72 cm². Therefore, the area is 72 cm².

Question 10

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 11

A triangle has a base of 16 cm and a height of 12 cm. What is its area?

Accepted Answer

Step 1: Use the formula for area of a triangle: Area = (1/2) × base × height. Step 2: Substitute values: Area = (1/2) × 16 × 12 = (1/2) × 192 = 96 cm². Therefore, the area is 96 cm².

Question 12

An equilateral triangle has a side length of 10 cm. What is its perimeter?

Accepted Answer

Step 1: An equilateral triangle has all three sides equal. Step 2: Perimeter = 3 × side length = 3 × 10 = 30 cm. Therefore, the perimeter is 30 cm.

Question 13

A parallelogram has a base of 24 cm and a height of 15 cm. If one of its sides is 20 cm, what is the perimeter of the parallelogram?

Accepted Answer

Step 1: In a parallelogram, opposite sides are equal. So if one side is 24 cm (base), the opposite side is also 24 cm. Similarly, if another side is 20 cm, the opposite side is also 20 cm. Step 2: Perimeter = 2(base + side) = 2(24 + 20) = 2(44) = 88 cm. Note: The height is given but not needed to find the perimeter—it would be used only if area was asked. Therefore, the perimeter is 88 cm.

Question 14

A right-angled triangle has legs of length 9 cm and 12 cm. What is the length of its hypotenuse?

Accepted Answer

Step 1: Use the Pythagorean theorem: c² = a² + b², where a and b are the legs and c is the hypotenuse. Step 2: Substitute values: c² = 9² + 12² = 81 + 144 = 225. Step 3: Take the square root: c = √225 = 15 cm. Therefore, the hypotenuse is 15 cm.

Question 15

A parallelogram has base 18 cm and height 10 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for area of a parallelogram: A = base × height. Step 2: Substitute base = 18 cm and height = 10 cm. Step 3: A = 18 × 10 = 180 cm². Therefore, the area is 180 cm².

Question 16

The area of a triangle is 24 cm² and its base is 6 cm. What is the height of the triangle?

Accepted Answer

Step 1: Use the area formula: Area = (1/2) × base × height. Step 2: Rearrange to find height: height = (2 × Area) ÷ base. Step 3: Substitute: height = (2 × 24) ÷ 6 = 48 ÷ 6 = 8 cm. Therefore, the height is 8 cm.

Question 17

A parallelogram has a base of 24 cm and a height of 15 cm. If the base is increased by 8 cm while the height remains the same, by what percentage does the area increase?

Accepted Answer

Step 1: Original area of parallelogram = base × height = 24 × 15 = 360 cm². Step 2: New base = 24 + 8 = 32 cm. New area = 32 × 15 = 480 cm². Step 3: Increase in area = 480 - 360 = 120 cm². Step 4: Percentage increase = (120 / 360) × 100 = 33.33% or 33⅓%.

Question 18

The area of a triangle is 60 cm² and its base is 15 cm. What is the height of the triangle?

Accepted Answer

Step 1: Use the triangle area formula: Area = (1/2) × base × height. Step 2: Rearrange to find height: height = (2 × Area) / base. Step 3: Substitute values: height = (2 × 60) / 15 = 120 / 15 = 8 cm. Therefore, the height is 8 cm.

Question 19

A triangle has sides of length 5 cm, 12 cm, and 13 cm. What is its area using Heron's formula?

Accepted Answer

Step 1: Calculate the semi-perimeter: s = (5 + 12 + 13) ÷ 2 = 30 ÷ 2 = 15 cm. Step 2: Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)] = √[15 × 10 × 3 × 2] = √[900] = 30 cm². Therefore, the area is 30 cm².

Question 20

Two lines intersect each other. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (they add up to 180°). Step 2: If one angle is 65°, then the adjacent angle = 180° − 65° = 115°. Therefore, the answer is 115°.

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