Question : 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?
Option 1: 7.5 cm
Option 2: 8 cm
Option 3: 5 cm
Option 4: 6 cm

Question

Question : 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?

Option 1: 7.5 cm

Option 2: 8 cm

Option 3: 5 cm

Option 4: 6 cm

Team Careers360 · Accepted Answer

Correct Answer: 5 cm

Solution : The volume of a hemisphere $ = \frac{2}{3}\pi r^3$
The volume of a cylinder $ = \pi r^2 h$
Where $r$ is the base radius and $h$ is the height.
Given that the radius of the hemisphere is 30 cm and the height of the cylindrical glass is 10 cm.
Equate the volume of the hemisphere to the volume of the cylindrical glass multiplied by the number of times the glass is poured into the bowl (72 times) to find the base radius of the cylindrical glass.
$⇒\frac{2}{3}\pi (30)^3 = 72 imes \pi r^2 imes 10$
$⇒r = \sqrt{\frac{2 imes (30)^3}{3 imes 72 imes 10}} = 5$
Hence, the correct answer is 5 cm.

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Question : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?Option 1: 196 cmOption 2: 486 cmOption 3: 224 cmOption 4: 384 cm

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Question : Find the weight of a cylindrical iron container with a base of radius 12.6 cm and height is 4 m, where the weight of 1 cm2 of iron is 2 grams.Option 1: 299.284 kgOption 2: 199.584 kgOption 3: 399.168 kgOption 4: 499.482 kg

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