A cone has radius r cm and height h cm - OCR - GCSE Maths - Question 18 - 2019 - Paper 6
Question 18
A cone has radius r cm and height h cm.
The height is three times the radius.
The volume of the cone is 2100 cm³.
Calculate the radius of the cone.
[The volume V ... show full transcript
Worked Solution & Example Answer:A cone has radius r cm and height h cm - OCR - GCSE Maths - Question 18 - 2019 - Paper 6
Step 1
Calculate the height in terms of the radius
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Answer
Given that the height (h) is three times the radius (r), we can express this as:
[ h = 3r ]
Step 2
Use the volume formula for the cone
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Answer
The volume of the cone is given by:
[ V = \frac{1}{3} \pi r^2 h ]
Substituting the volume and the expression for height:
[ 2100 = \frac{1}{3} \pi r^2 (3r) ]
This simplifies to:
[ 2100 = \pi r^3 ]
Step 3
Solve for the radius
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Answer
Rearranging the equation gives:
[ r^3 = \frac{2100}{\pi} ]
To find (r), take the cube root:
[ r = \sqrt[3]{\frac{2100}{\pi}} \approx 8.74 \text{ cm} ]
