Question

State true or false:

The total surface area of a hollow cylinder, which is open from both the sides, is $3575c{m}^2;$ area of its base ring is $357.5c{m}^2$ and its height is $14cm$, then the thickness of the cylinder is $3.5cm$.

• A. True
• B. False

Answer 1

Answer: (A)

Let us take outer radius as $R$ and inner radius as $r$.

Area of ring is $A=\pi (R^2-r^2)$

$357.5=\pi (R^2-r^2)$

$357.5÷\pi =(R^2-r^2)$ --- (1)

Multiplying eq(1) by $10$, we get

$3575÷\pi =10\times (R^2-r^2)$ ----(2)

Surface area of hollow cylinder $=2\pi Rh+2\pi rh+2\pi (R^2-r^2)$

$3575=2\pi Rh+2\pi rh+2\pi (R^2-r^2)$

$3575÷\pi =2Rh+2rh+2(R^2-r^2)$ ----(3)

Equation eq (2) and eq (3), we get

$10(R^2-r^2)=2Rh+2rh+2(R^2-r^2)$

$8(R^2-r^2)=2Rh+2rh$

$8(R^2-r^2)=28(R+r)$

$(R-r)=3.5$

Thickness of the cylinder $=3.5cm$