Question

# A cylindrical jar of radius 12 cm contains oil. Iron spheres each of radius 3 cm are immersed in the oil. How many such spheres are needed to raise the oil by 4 cm?16 8 10 32

Solution

## The correct option is A 16 Note that, Volume of the cylinder with height  4 cm = n× Volume of one iron sphere, where n is the required number of iron spheres. Let R and r be the radii of the cylindrical jar and the iron sphere respectively. i.e., R=12 cm and r=3 cm Then we have,πR2h=n×43π×r3 ⟹π122×4=n×43π×33 ⟹n=16 ​

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The text passage contains a mathematical word problem involving the volume of a cylinder and spheres, followed by a solution that provides the answer to the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Question

# A cylindrical jar of radius 12 cm contains oil. Iron spheres each of radius 3 cm are immersed in the oil. How many such spheres are needed to raise the oil by 4 cm?16 8 10 32

Solution

## The correct option is A 16 Note that, Volume of the cylinder with height  4 cm = n× Volume of one iron sphere, where n is the required number of iron spheres. Let R and r be the radii of the cylindrical jar and the iron sphere respectively. i.e., R=12 cm and r=3 cm Then we have,πR2h=n×43π×r3 ⟹π122×4=n×43π×33 ⟹n=16 ​

Suggest corrections
user
The text passage contains a mathematical word problem involving the volume of a cylinder and spheres, followed by a solution that provides the answer to the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER