Q.If a hemispherical basin with a diameter of 150 cm can hold 120 times more water than a cone with a height of 15 cm, then what is the diameter of that cone? (a) 27 cm (b) 24 cm (c) 25 cm (d) 26 cm
Answer: C
Let the radius of the cone be \(r\) cm. \[ \therefore\ \frac{2}{3}\pi \left(\frac{150}{2}\right)^3 = 120\pi r^2 \times 15 \] i.e., \[ \frac{2 \times 75 \times 75 \times 75}{3} = 120 \times 15 \times r^2 \] Simplifying, \[ r^2 = \frac{2 \times 75 \times 75 \times 75}{3 \times 120 \times 15} = \frac{625}{4} \] \[ r = \frac{25}{2} \] \(\therefore\) The diameter of the cone = \(2 \times \frac{25}{2} = 25\) cm.
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