Question

The curved surface area of a cylinder is 264m² and its volume is 924m⁴ . The diameter of the cylinder is?

Answer 1

CSA = 2πrh

2πrh = 264

πrh = 132

Volume = πr²h

πr²h = 924

132r = 924

r = 7

Diameter = 2r = 14 m

Answer 2

Given:

• The curved surface area of a cylinder is 264m²
• the volume of the cylinder is volume is 924m³

To find :

• the diameter of the cylinder

Solution:

${\purple{ \underline{ \mathfrak{ \dag \: As \: we \: know \: that : }}}}$

• C.S.A Of the cylinder is ${\bf{\green{26{4m}^{2}}}}$

• Volume of the cylinder is ${\bf{\green{92{4m}^{2}}}}$

Now, the formulas of them are ${\downarrow}$

$\longrightarrow\blue{ \underline{ \boxed{ \pink{ \mathfrak{curved \: surface \: area \: = 2\pi \: r h}}}} \bigstar}$

$\longrightarrow\blue{ \underline{ \boxed{ \pink{ \mathfrak{ volume = \pi \: {r}^{2}h }}}} \bigstar}$

hence,

$\longrightarrow \sf \: \frac{\pi {r}^{2}h }{2\pi \: rh} = \frac{924}{264} \\ \\ \\ \longrightarrow \sf \: \frac{ \cancel\pi {r}^{2}\cancel{h} }{2\cancel\pi \: r\cancel{h}} = \frac{924}{264} \\ \\ \\ \longrightarrow \sf \: \frac{ {r}^{2} }{2r} = \cancel\frac{924}{264} \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: \frac{ \cancel{{r}^{2}} }{ 2\cancel{ r}} = 3.5 \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: \frac{r}{2} = 3.5 \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: r \: = 3.5 \times 2 \: \: \: \: \\ \\ \\ \longrightarrow \sf \: r = 7m \bigstar \: \: \: \:$

We know,

• diameter = 2(radius)

➪ diameter = $\bf\green {14m}$