Question 1

A cylinder and a cone have the same radius of 5 cm and the same height of 12 cm. What is the ratio of their volumes?

Accepted Answer

Step 1: Volume of cylinder = πr²h = π × 5² × 12 = 300π cm³. Step 2: Volume of cone = (1/3)πr²h = (1/3) × π × 5² × 12 = 100π cm³. Step 3: Ratio = 300π : 100π = 3 : 1. Therefore, the answer is 3:1.

Question 2

The total surface area of a sphere is 616 cm². What is its radius? (Use π = 22/7)

Accepted Answer

Step 1: Total Surface Area of sphere = 4πr². Step 2: Given 4πr² = 616. Step 3: 4 × (22/7) × r² = 616. Step 4: (88/7) × r² = 616. Step 5: r² = 616 × (7/88) = 4312/88 = 49. Step 6: r = 7 cm. Therefore, the answer is 7 cm.

Question 3

A cone has a base radius of 8 cm and height of 15 cm. What is its slant height?

Accepted Answer

Step 1: In a cone, slant height l, radius r, and height h form a right triangle. Step 2: By Pythagoras theorem: l² = r² + h². Step 3: l² = 8² + 15² = 64 + 225 = 289. Step 4: l = √289 = 17 cm. Therefore, the answer is 17 cm.

Question 4

The volume of a sphere is 288π cm³. What is its radius?

Accepted Answer

Step 1: Volume of sphere = (4/3)πr³. Step 2: Given (4/3)πr³ = 288π. Step 3: Divide both sides by π: (4/3)r³ = 288. Step 4: Multiply by 3/4: r³ = 288 × (3/4) = 216. Step 5: r = ∛216 = 6 cm. Therefore, the answer is 6 cm.

Question 5

The curved surface area of a cone is 550 cm² and its slant height is 25 cm. What is the radius of the base of the cone? (Use π = 22/7)

Accepted Answer

Step 1: Curved surface area of cone = πrl, where r is radius and l is slant height. Step 2: 550 = (22/7) × r × 25. Step 3: 550 = (550/7) × r. Step 4: r = 550 × (7/550) = 7 cm. Therefore, the radius is 7 cm.

Question 6

A sphere has a radius of 6 cm. If the radius is increased by 50%, by what percentage does the volume increase? (Use π = 22/7)

Accepted Answer

Step 1: Original volume V₁ = (4/3)πr³ = (4/3)π(6)³ = (4/3)π × 216 = 288π cm³. Step 2: New radius = 6 + 50% of 6 = 6 × 1.5 = 9 cm. Step 3: New volume V₂ = (4/3)π(9)³ = (4/3)π × 729 = 972π cm³. Step 4: Percentage increase = [(972π - 288π)/(288π)] × 100 = (684/288) × 100 = 237.5%. Therefore, the answer is 237.5%.

SBI Clerk Geometry & Mensuration Questions

SBI Clerk Geometry & Mensuration — Past Exam Questions

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