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Answer :
To find the radius of the base of a right circular cylinder, we can use the formula for the curved surface area (CSA) of a cylinder. The CSA of a cylinder is given by:
[tex]\[ \text{CSA} = 2 \pi r h \][/tex]
where [tex]\( r \)[/tex] is the radius, [tex]\( h \)[/tex] is the height, and [tex]\( \pi \)[/tex] is approximately 3.14159.
We know from the problem that:
- The height [tex]\( h = 14 \)[/tex] cm
- The curved surface area [tex]\( \text{CSA} = 176 \)[/tex] sq. cm
We need to solve for the radius [tex]\( r \)[/tex]. Let's rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{\text{CSA}}{2 \pi h} \][/tex]
Substitute the known values into the formula:
[tex]\[ r = \frac{176}{2 \times \pi \times 14} \][/tex]
Calculate the denominator:
[tex]\[ 2 \times \pi \times 14 \approx 87.9646 \][/tex]
Now divide the curved surface area by this result:
[tex]\[ r = \frac{176}{87.9646} \approx 2.000805 \][/tex]
Therefore, the radius of the base of the cylinder is approximately 2.00 cm.
[tex]\[ \text{CSA} = 2 \pi r h \][/tex]
where [tex]\( r \)[/tex] is the radius, [tex]\( h \)[/tex] is the height, and [tex]\( \pi \)[/tex] is approximately 3.14159.
We know from the problem that:
- The height [tex]\( h = 14 \)[/tex] cm
- The curved surface area [tex]\( \text{CSA} = 176 \)[/tex] sq. cm
We need to solve for the radius [tex]\( r \)[/tex]. Let's rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{\text{CSA}}{2 \pi h} \][/tex]
Substitute the known values into the formula:
[tex]\[ r = \frac{176}{2 \times \pi \times 14} \][/tex]
Calculate the denominator:
[tex]\[ 2 \times \pi \times 14 \approx 87.9646 \][/tex]
Now divide the curved surface area by this result:
[tex]\[ r = \frac{176}{87.9646} \approx 2.000805 \][/tex]
Therefore, the radius of the base of the cylinder is approximately 2.00 cm.
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