Question

The thickness of a hollow cylinder is 6 $cm$ and the sum of internal and external radii is 14 $cm$. If the total surface area of the cylinder is $1760c{m}^2,$ then the height of the cylinder is

• A. 7 cm
• B. 8 cm
• C. 21 cm
• D. 14 cm

Answer 1

The correct option is D 14 cm

Let $r_1$ and $r_2$ be the external and internal radii of the hollow cylinder and $h$ be its height.
Given that, $r_1+r_2=14cm$.
Thickness of the hollow cylinder, $(r_1–r_2)=6cm$
Total surface area of the cylinder $=1760c{m}^2$
$\Rightarrow 2\pi (r_1+r_2)h+2\pi (r_1^2-r_2^2)=1760$
$\Rightarrow 2\pi \left[\right(r_1+r_2)h+(r_1+r_2\left)\right(r_1-r_2\left)\right]=1760$
$\Rightarrow 2\times \frac{22}{7}\times 14(h+6)=1760$
$\Rightarrow 88(h+6)=1760$
$\Rightarrow h+6=20$
$\Rightarrow h=14cm$
Therefore, the height of the cylinder is 14 $cm$.
Hence, the correct answer is option (d).