Question

CSA of a pillar is 264m2.Find the diameter of the pillar if its
height is 14m.​

Answer 1

• The diameter of the cylindrical pillar = 6 m.

Given :

• The curved surface area (C.S.A.) of the cylindrical pillar = 264 m².
• The height of the pillar = 14 m.

To Find :

• the diameter of the pillar.

Solution :

Let,

The diameter of the pillar be x.

Given,

The curved surface area (C.S.A.) of the cylindrical pillar = 264 m².

We know that,

Curved surface area of the cylinder = 2πrh

That means,

$\: \: \bullet \rm\: \: 2\pi rh = 264 \: {m}^{2} \\ \\ : \implies \rm 2 \times \dfrac{22}{ \not7} \times r \times \not{14} \: m = 264 \: {m}^{2} \\ \\ : \implies \rm 2 \times 22 \times r \times 2 = 264 \: {m}^{2} \\ \\ : \implies \rm 88r = 264 \: {m}^{2} \\ \\ : \implies \rm r = \dfrac{264 \: { \not{m}}^{2} }{88 \: \not{m}} \\ \\ : \implies \rm r = \dfrac{132}{44} \: m \\ \\ : \implies \rm r = \dfrac{66}{22} \: m \\ \\ : \implies \rm r = \dfrac{33}{11} \: m \\ \\ : \implies \rm r = 3 \: m \\ \\ \: \: \rm \therefore \: \: radius = 3 \: m$

Hence, the radius of the pillar is 3 m.

We know that,

• d = 2r

Where,

• d = diameter.
• r = radius.

$: \implies \rm d = 2\times 3 \: m \\ \\ : \implies \rm d = 6 \: m$

Hence,

The diameter of the cylindrical pillar is 6 m.

Answer 2

$\huge\bold{\gray{\sf{Given:}}}$

C.S.A of a pillar is $\bold{264}{m}^2$

Height is 14m

$\huge\bold{\gray{\sf{To\:Find:}}}$

Diameter of the pillar

$\huge\tt{\bold{\gray{\sf{\underline{\underline{Answer᎓}}}}}}$

Explanation:

$\bold{\boxed{\red{C.S.A \: of a \: cylinder = 2\pi \: rh}}}$

Now come to the question:-

$= > 2\pi \: rh = 264$

$= > 2 \times \frac{22}{7} \times r \times 14 = 264$

$= > 44 \times 2 \times r = 264$

$= > 88r = 264$

$= > r = \frac{264}{88} = \frac{132}{44} = \frac{66}{22} = 3$

$Radius = 3m$

We know that diameter is double of radius or radius is half of diameter.

$\bold{\boxed{\gray{\sf{D=2\times \:radius}}}}$

Diameter=2×3m=6m

Related Formulas:

$\bold{\boxed{TSA \: of \: cyclinder = 2\pi \: r(h + r)}}$

$\bold{\boxed{Volume \: of \: cyclinder = \pi {r}^{2} h}}$

Additional information:

• A cylinder is a three dimensional figure say 3D
• The bases of cylinder are congruent and parallel
• It is also called right circular cylinder when it's bases are circular.see figure 1.1