Question

The curved surface areas and the volume of a pillar are 264cm and 396 respectively. Find the diameter and the height of the pillar

Answer 1

$\huge{\mathbf{\red{\underline{Hola\: Mate}}}}$

$\huge{\mathbf{\blue{\underline{Solution:-}}}}$

$\large{\mathbf{\blue{\underline{Given:-}}}}$

$the \: curved \: surface \: area \: and \: volume \: of \: a \: pillar \: are \: 264m^{2} \: and \: 396m^{2}$

Let r and h be the radius of a pillar.

We know that,

$surface \: area \: of \: cylinder \: = 2\pi \: rh$

$volume \: of \: cylinder = \pi \: r{2} h$

Now, According to question,

$2\pi \: rh = 264$

$= > h = \frac{264}{2\pi \: r} \: .... ..........(1)$

$and$

$\pi \: r^{2} h = 396 \: .............(2)$

Substitute value of h from equation (1) in equation (2), we have,

$\pi \: r^{2} ( \frac{264}{2\pi \: r} ) = 396$

$= > r = \frac{369 \times 2}{264} = 3$

$\large{\boxed{\boxed{\mathbf{\red{r = 3m}}}}}$

$\large{\boxed{\boxed{\mathbf{\red{diameter = 6m}}}}}$

Substitute value of r in equation (1), we have,

$h = \frac{264}{2\pi \times 3} = \frac{44}{\pi} = \frac{44 \times 7}{22} = 14m$

$\large{\boxed{\boxed{\mathbf{\red{h = 14m}}}}}$

Hence the diameter and height of pillar is 6m and 14m.

$\large{\boxed{\boxed{\mathbf{\red{Hope\: It\: Helps}}}}}$

$\huge{\mathbf{\red{\underline{Thanks}}}}$

Answer 2

$\huge\bf\pink{\mid{\overline{\underline{Your\: Answer}}}\mid}$

Diameter = 6 m

Height = 42 m

step-by-step explanation:

Let the radius and height of the cylindrical pillar be 'r' and 'h' respectively.

Now,

it us given that,

CSA = 264 ${m}^{2}$

But,

we know that,

CSA = 2πrh

=> 2πrh = 264

=> πrh = 132 ....................(i)

Now,

also,

volume of pillar = 396 ${m}^{3}$

But,

we know that,

Volume = π${r}^{2}$h

=> π${r}^{2}$h = 396

=> r(πrh) = 396

putting the value of πrh from eqn (i),

we get,

=> 132r = 396

=> r = 396/132

=> r = 3 m

Now,

putting the value of r in eqn (i),

we get,

=> 3π h = 132

=> h = 132/3π

=> h = (132× 7)/(22× 3)

=> h = 42/ 3 m

=> h = 14 m

Hence,

Diameter = 6 m

Height = 14 m