Question

The height of a right circular cylinder is $5$ and the diameter of its base is $4$. What is the distance from the center of one base to a point on the circumference of the other base?

• A. $3$
• B. $5$
• C. $\sqrt{29}$
• D. $\sqrt{33}$

Answer 1

The correct option is C $\sqrt{29}$

Given

Height of the right circular cylinder ${(}^{\prime }{h}^{\prime })$ $=$ $5$

Diameter of its base $=$ $4$

Radius of its base ${(}^{\prime }{r}^{\prime })$ $=$ $\frac{1}{2}$ $\times$ Diameter of its base

$=$ $\frac{1}{2}$ $\times$ $4$

$=$ $2$

Let the distance from the center of one base to the point on the circumference of other base be ${}^{\prime }{l}^{\prime }$.

We can observe that

(Height of the cylinder), (radius of the cylinder) and (the line joining the center of one base to the point on the circumference of other base) form a right-angled triangle with hypotenuse of length ${}^{\prime }{l}^{\prime }$

To find ${}^{\prime }{l}^{\prime }$,

By Pythagoras theorem,

$l^2$ $=$ $h^2$ $+$ $r^2$

$\Rightarrow l^2$ $=$ $5^2$ $+$ $2^2$

$\Rightarrow l^2$ $=$ $25$ $+$ $4$

$\Rightarrow l^2$ $=$ $29$

$\Rightarrow l$ $=$ $\sqrt{29}$

$\Rightarrow l$ $=$ $5.39$

Therefore, distance from the center of one base to a point on the circumference of the other base is ${}^{\prime }$$\sqrt{29}$ ${}^{\prime }$${}^{\prime }\left(approximately5.39\right)$${}^{\prime }$.