A hemispherical bowl of radius 30 cm is filled with water by using a cylindrical glass If the water ...........

Quantitative Aptitude (MTS) Mensuration 2D

A hemispherical bowl of radius 30 cm is filled with water by using a cylindrical glass. If the water from the cylindrical glass is

poured 72 times to fill the bowl completely and the height of the glass is 10 cm, then what is the base radius of the cylindrical

glass?

This questions was previously asked in

SSC MTS 11th July 2022 Shift-2

View All SSCMTS Previous Year Papers

6 cm

7.5 cm

8 cm

5 cm

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Explanation:

- Volume of the hemispherical bowl: The formula for the volume of a hemisphere is \((2/3)pr^3\). For a radius of 30 cm, the volume is \((2/3)p(30)^3 = 18,000p\) cubic cm.

- Volume of the cylindrical glass: The formula is \(\pr^2h\), where \(r\) is the base radius and \(h\) is the height. Given \(h = 10\) cm, the volume is \(\pr^2(10)\) cubic cm.

- Total volume of water poured: Since water is poured 72 times, the total volume is \(72pr^2(10)\).

- Setting this equal to the volume of the bowl gives: \(720pr^2 = 18,000p\).

- Solving for \(r^2\): \(r^2 = 25\) gives \(r = 5\) cm.

- Option 4: 5 cm is the correct answer.

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