Question : A well of 3 m in diameter is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Option 1: 4.25 m
Option 2: 2.25 m
Option 3: 1.125 m
Option 4: 1.75 m
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Correct Answer: 1.125 m
Solution : Given: A well of 3 m in diameter is dug 14 m deep. Here, $h_1=14\ m$, $r_1=\frac{3}{2}\ m,$ and $r_2=4+\frac{3}{2}=\frac{11}{2}\ m$ We know that the volume of the cylinder = $\pi r^2h$ Let the height of the embankment be $h_2\ m$. According to the question, $\pi\times (r_1)^2\times h= \pi\times (r_2^2-r_1^2)\times h$ $⇒\pi\times (\frac{3}{2})^2\times 14= \pi\times [(\frac{11}{2}^2)-(\frac{3}{2})^2]\times h$ $⇒\frac{9}{4}\times 14=(\frac{121-9}{4})\times h$ $⇒\frac{9}{4}\times 14= \frac{112}{4}\times h$ $⇒h= \frac{9}{8}$ $⇒h= 1.125$ m Hence, the correct answer is 1.125 m.
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Question : A well with an inner radius of 3 m, is dug 6 m deep. The soil taken out of it has been spread evenly all around it to a width of 2 m to form an embankment. The height (in m) of the embankment is:
Option 1: $4 \frac{1}{2}$
Option 2: $4 \frac{1}{4}$
Option 3: $3 \frac{1}{4}$
Option 4: $3 \frac{3}{8}$
Question : The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.
Option 1: 8 m
Option 2: 0.04 m
Option 3: 0.08 m
Option 4: 0.008 m
Question : A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm. Find the length of the wire.
Option 1: 143 m
Option 2: 108 m
Option 3: 324 m
Option 4: 234 m
Question : The outer and inner diameters of a circular path are 728 m and 700 m respectively. The breadth of the path is:
Option 1: 7 m
Option 2: 28 m
Option 3: 14 m
Option 4: 20 m
Question : The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?
Option 1: 100
Option 2: 400
Option 3: 500
Option 4: 1000
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