Question

The ratio of height of a right circular solid cylinder and length of radius of base is 3:1. If the volume of the cylinder is 1029π cubic cm, what will be the total surface area of the cylinder?
Moderator please answer. ​

Answer 1

EXPLANATION.

Ratio of height of a right circular solid cylinder and length of a base = 3:1.

volume of cylinder = 1029π.

As we know that,

Height of a right circular solid cylinder = 3r.

Radius of a right circular solid cylinder = r.

As we know that,

Volume of a solid cylinder = πr²h.

⇒ πr²h = 1029π.

⇒ π will get cancel, we get.

⇒ r²h = 1029.

⇒ r²(3r) = 1029.

⇒ 3r³ = 1029.

⇒ r³ = 1029/3.

⇒ r³ = 343.

⇒ r³ = 7 X 7 X 7.

⇒ r = 7 cm.

Put the value of r = 7 in equation, we het.

Height = 3r.

Height = 3(7) = 21 cm.

As we know that,

Formula of : Total surface area.

⇒ T.S.A = 2πr(h + r).

⇒ T.S.A = 2 X 22/7 X 7 (21 + 7).

⇒ T.S.A = 44(28).

⇒ T.S.A = 1232cm².

Answer 2

$\sf \Large Solution!!$

Let the ratio be 3x and x.

Height = 3x

Radius = x

Now, the volume of the cylinder is given. So, we'll find out the value of x by using the formula which is used to calculate the volume of a cylinder.

Volume of cylinder = $\sf \pi r^{2}h$

$\sf 1029\cancel{\pi }=\cancel{\pi }\times x^{2}\times 3x$

$\sf 1029=3x^{3}$

$\sf \dfrac{1029}{3}=x^{3}$

$\sf x^{3}=343$

$\sf x=7\:cm$

Putting the value of x in height and radius.

Height = 3x = 3 × 7 cm = 21 cm

Radius = x = 7 cm

Now we just need to apply a formula to find the total surface area (TSA).

$\sf TSA=2\pi r(r+h)$

$\sf TSA=2\times \dfrac{22}{7}\times 7\:cm(7\:cm+21\:cm)$

$\sf TSA=2\times \dfrac{22}{\cancel{7}}\times \cancel{7}\:cm\times 28\:cm$

$\sf TSA=2\times 22\times 28\:cm^{2}$

$\boxed{\blue{\sf TSA=1232\:cm^{2}}}$