On a circular metal plate of uniform thickness, 16 holes, each of diameter 2 cm, are made. If the plate thereby has lost one-ninth of its original weight, then what is the diameter of the plate?
24 cm
Since thickness and density are uniform, weight lost is proportional to area removed. Area of the 16 holes (each radius 1 cm) = \(16 \times \pi (1)^2 = 16\pi\ \text{cm}^2\). This equals one-ninth of the plate's area: \(16\pi = \frac{1}{9}\pi R^2 \Rightarrow R^2 = 144 \Rightarrow R = 12\ \text{cm}\). So the diameter of the plate = \(2R = 24\ \text{cm}\).
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Statement II: Length BC is an integer.
Which one of the following is correct in respect of the above Question and Statements?
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Important Questions from 2-D Mensuration
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The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
