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Volume & Surface Areas Questions and Answers

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171.

If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is

Answer: B

Two hemispheres joined along their flat faces make a complete sphere, and the two flat faces vanish inside it.

\[ \text{curved surface} = 2 \times 2\pi r^{2} = 4\pi r^{2} \]

which is exactly the surface area of a sphere of radius \( r \). The \( 3\pi r^{2} \) option is the total surface of a single solid hemisphere, base included - but that base is no longer exposed once the two are joined.

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172.

Radius of a circle is increased by 6%, determine the increase in area of the circle.

Answer: B

Area of a circle is \( \pi r^{2} \), so a 6% rise in the radius acts through the square.

\[ \frac{A'}{A} = \left(\frac{1.06r}{r}\right)^{2} = (1.06)^{2} = 1.1236 \]

\[ \text{increase} = 1.1236 - 1 = 0.1236 = 12.36\% \]

Doubling the percentage to 12% misses the square term \( \left(\tfrac{6}{100}\right)^{2} = 0.36\% \). The exact rule is \( 2x + \tfrac{x^{2}}{100} \).

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173.

If a cuboid is 3.2 cm high, 8.9cm long and 4.7 wide then total surface area is

Answer: A

A cuboid has three pairs of identical faces.

\[ \text{TSA} = 2(lb + bh + hl) \]

\[ = 2\left(8.9 \times 4.7 + 4.7 \times 3.2 + 3.2 \times 8.9\right) \]

\[ = 2(41.83 + 15.04 + 28.48) = 2(85.35) \]

\[ = 170.7 \text{ cm}^{2} \]

Each of the three products must appear twice; summing them once gives 85.35, exactly half the answer.

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174.

By converting 2500000mm³ into cm³, answer will be

Answer: B

A centimetre is 10 millimetres, so a cubic centimetre is \( 10^{3} \) cubic millimetres.

\[ 1 \text{ cm}^{3} = 1000 \text{ mm}^{3} \]

\[ 2{,}500{,}000 \text{ mm}^{3} = \frac{2{,}500{,}000}{1000} = 2500 \text{ cm}^{3} \]

Dividing by 10 or by 100 instead - the length and area factors - gives the two nearby distractors.

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