Question 1

A cylinder has a radius of 7 cm and height of 10 cm. What is the total surface area of the cylinder? (Use π = 22/7)

Accepted Answer

Step 1: Total Surface Area of cylinder = 2πr(r + h)
Step 2: Substitute r = 7 cm and h = 10 cm
TSA = 2 × (22/7) × 7 × (7 + 10)
Step 3: TSA = 2 × 22 × 1 × 17
Step 4: TSA = 44 × 17 = 748 cm²
Therefore, the total surface area is 748 cm².

Question 2

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 for area of a circle: A = πr². Step 2: Substitute r = 7 cm and π = 22/7. Step 3: A = (22/7) × 7 × 7 = (22/7) × 49 = 22 × 7 = 154 cm². Therefore, the area is 154 cm².

Question 3

A ray stands on a straight line. If the two angles formed on either side of the ray are in the ratio 2 : 3, what is the measure of the larger angle?

Accepted Answer

Step 1: Since the ray stands on a straight line, the two angles form a linear pair and their sum = 180°. Step 2: Let the angles be 2x and 3x. Then 2x + 3x = 180° → 5x = 180° → x = 36°. Step 3: The larger angle = 3x = 3 × 36° = 108°. Therefore, the answer is 108°.

Question 4

A solid metallic sphere of radius 6 cm is melted and recast into a solid cylinder of radius 4 cm. Find the height of the cylinder (in cm).

Accepted Answer

Step 1: Find the volume of the sphere using the formula V = (4/3)πr³
Volume of sphere = (4/3)π(6)³ = (4/3)π(216) = 288π cm³

Step 2: The sphere is melted and recast into a cylinder, so the volumes are equal.
Volume of cylinder = πr²h
288π = π(4)²h
288π = 16πh

Step 3: Solve for h
h = 288π/(16π) = 288/16 = 18 cm

Therefore, the height of the cylinder is 18 cm.

Question 5

The diagonals of a rhombus are 24 cm and 10 cm. What is the perimeter of the rhombus?

Accepted Answer

Step 1: In a rhombus, diagonals bisect each other at right angles. So half-diagonals are 12 cm and 5 cm. Step 2: Each side of the rhombus = √(12² + 5²) = √(144 + 25) = √169 = 13 cm. Step 3: Perimeter = 4 × 13 = 52 cm. Therefore, answer is 52 cm.

Question 6

A solid metallic cylinder of radius 6 cm and height 28 cm is melted and recast into small solid cones, each of radius 2 cm and height 3 cm. How many such cones are formed?

Accepted Answer

Step 1: Volume of cylinder = πr²h = π × 6² × 28 = 1008π cm³. Step 2: Volume of each small cone = (1/3)πr²h = (1/3) × π × 2² × 3 = 4π cm³. Step 3: Number of cones = Volume of cylinder / Volume of cone = 1008π / 4π = 252. Therefore, answer is 252.

SSC CHSL Geometry & Mensuration Questions

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