Question
A solid cylinder has a total surface area of $462 cm^2$. Its curved surface area is one-third of its total surface area.
Find the radius and height of the cylinder.
Find the radius and height of the cylinder.
✓
Answer
Given that Curved or lateral surface area $=13 \times$ total surface area
$2 \pi rh =\frac{1}{3}\left(2 \pi rh +2 \pi r ^2\right)$
$4 \pi rh =2 \pi r ^2$
$2 h= r$
Total surface area $=462 cm^2$ Curved surface area
$=\frac{1}{3} \times 4622 \pi rh =154$
$2 \times 3.14 \times 2 \times h ^2=154$
$h ^2=\frac{49}{4}$
$h =\frac{49}{4} cm$
$=\frac{7}{2} cm$
Now $r =2 h$ Therefore $r =2 \times 72 cm=7 cm$
The height and the radius of the cylinder is $\frac{7}{2} cm$ and 7 cm respectively.
$2 \pi rh =\frac{1}{3}\left(2 \pi rh +2 \pi r ^2\right)$
$4 \pi rh =2 \pi r ^2$
$2 h= r$
Total surface area $=462 cm^2$ Curved surface area
$=\frac{1}{3} \times 4622 \pi rh =154$
$2 \times 3.14 \times 2 \times h ^2=154$
$h ^2=\frac{49}{4}$
$h =\frac{49}{4} cm$
$=\frac{7}{2} cm$
Now $r =2 h$ Therefore $r =2 \times 72 cm=7 cm$
The height and the radius of the cylinder is $\frac{7}{2} cm$ and 7 cm respectively.
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