Question : 2 cm of rain has fallen on a square km of land. Assuming that 50% of the raindrops could have been collected and contained in a pool having a 100 m × 10 m base, by what level would the water level in the pool have increased?
Option 1: 1 km
Option 2: 10 m
Option 3: 10 cm
Option 4: 1 m
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Correct Answer: 10 m
Solution : The volume of rainwater received by the land = Area of the base × height = $1000 \times 1000 \times \frac{2}{100}$ = $20000$ m3 Volume of 50% of raindrop stored in the pool = $\frac{20000}{2}$ = 10000 m3 $\therefore$ Required water level in pool increased $=\frac{\text{Volume of raindrop stored}}{\text{Area of base of pool}}=\frac{10000}{100\times10}= 10$ m Hence, the correct answer is 10 m.
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Question : If the length of a certain rectangle is decreased by 4 cm and breadth is increased by 2 cm, it would result in a square of the same area. What is the perimeter of the original rectangle?
Option 1: 15 cm
Option 2: 24 cm
Option 3: 20 cm
Option 4: 10 cm
Question : The base of a right pyramid is square of side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is:
Option 1: 400 cm2
Option 2: 460 cm2
Option 3: 260 cm2
Option 4: 360 cm2
Question : The base of a right pyramid is a square of side $8 \sqrt{2}$ cm and each of its slant edges is of length 10 cm. What is the volume (in cm$^3$) of the pyramid?
Option 1: $256$
Option 2: $224$
Option 3: $426 \frac{2}{3}$
Option 4: $96 \sqrt{2}$
Question : The base of a solid right prism of height 10 cm is a square and its volume is 160 cm3. What is the total surface area of the prism (in cm2)?
Option 1: 200
Option 2: 176
Option 3: 192
Option 4: 180
Question : What is the total surface area of a pyramid whose base is a square with a side 8 cm and the height of the pyramid is 3 cm?
Option 1: 169 cm2
Option 2: 121 cm2
Option 3: 144 cm2
Option 4: 184 cm2
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