Question

# The curved surface area of a right circular cylinder of height 14 cm is 88 $cm^2$. Find the diameter of the base of the cylinder.

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Now given that

Height of cylinder is=14cm

Curved surface area = 88 ${cm^2}$

Also curved surface area = $2\pi rh$

$\Rightarrow {\text{ 2}}\pi rh{\text{ = 88}}$

From this we can find the value of ‘r’ and by finding the value of ‘r’ we can determine the diameter of the cylinder.

$\Rightarrow r = {\text{ }}\dfrac{{88}}{{2\pi h}}$

${\text{or }}r = {\text{ }}\dfrac{{44}}{{\pi \times 14}}$

${\text{or }}r = {\text{ }}\dfrac{{22}}{{\pi \times 7}}$

${\text{or }}r = {\text{ 1}}cm{\text{ }}\left[ {\because {\text{ }}\pi {\text{ = }}\dfrac{{22}}{7}} \right]$

Now diameter of the base = 2r

$2r = 2 \times 1 = 2cm$

Note: - In this question we have found the value of radius of cylinder by equating the value of curved surface area of cylinder and its formula from there we get the value of radius then we find the value of diameter.