Class 9 Surface Area of a Sphere — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The formula for the surface area of a sphere of radius r is:

A4*pi*r²
B2*pi*r²
Cpi*r²
D $\frac{4}{3}$ *pi*r³

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Answer: A) 4*pi*r²

The surface area of a sphere of radius r is 4*pi*r².

\frac{4}{3}

*pi*r³ is its volume.

2. Which of these has the largest surface area, all with radius 5 cm? (CSA = curved surface area, TSA = total surface area)

AA sphere
BA hemisphere (CSA)
CA hemisphere (TSA)
DA flat circle

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Answer: A) A sphere

Sphere = 4*pi*r²; hemisphere TSA = 3*pi*r²; hemisphere CSA = 2*pi*r²; circle = pi*r². The sphere (4*pi*r²) is largest.

3. The number of pi*r² units in the surface area of a full sphere is:

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Answer: A) 4

4*pi*r² = 4 times pi*r², so the surface area equals 4 circles of the same radius.

4. A cricket ball and a tennis ball are both spheres.
The cricket ball has radius 3.6 cm and the tennis ball has radius 3.3 cm.
Which statement is correct about their surface areas?

AThe cricket ball has the larger surface area
BThe tennis ball has the larger surface area
CBoth have equal surface area
DCannot be decided without pi

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Answer: A) The cricket ball has the larger surface area

Surface area = 4*pi*r² increases with r. Since 3.6 > 3.3, the cricket ball has the larger surface area.

5. A spherical balloon's radius increases steadily from 5 cm to 7 cm.
Find the increase in its surface area (take pi = 22/7).

A301.71 cm²
B616 cm²
C314.29 cm²
D150.86 cm²

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Answer: A) 301.71 cm²

Initial SA = 4*(22/7)*25 = 314.29 cm². Final SA = 4*(22/7)*49 = 616 cm². Increase = 616 - 314.29 = 301.71 cm².

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