By converting 6800cm³ into ml, answer will be
Answer: A
The millilitre is defined as one cubic centimetre, so the two units are interchangeable and the number does not change.
\[ 1 \text{ cm}^{3} = 1 \text{ ml} \]
\[ 6800 \text{ cm}^{3} = 6800 \text{ ml} \]
The factor of 1000 belongs to the litre, not the millilitre: 6800 cm³ is 6.8 litres.
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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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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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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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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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