Question

$\huge\sf\fbox\purple{Question}$
The capacity of a closed cylindrical vessel of height 1m is15.4 liters. How many square meters of metal sheet would be needed to make it? (Assume π = 22/7)


spammers will be reported ❗​

Answer 1

Answer:

0.4708 m²

Step-by-step explanation:

Since the cylinder is a closed vessel, a metal sheet would be needed for the curved surface area and area of the two bases, top and bottom, that is TSA of the cylinder.

Hence, area of the metal sheet will be equal to TSA of the cylinder.

$\boxed{\rm TSA_{cylinder} = 2πr(r+h)}$

$\boxed{\rm Volume_{cylinder} = \pi r ^2 h}$

$\tt Capacity = 15.4 \: \: liters$

$\tt = \dfrac{15.4}{1000} \: m^3$

$\tt = 0.0154\: m^3$

$\tt Hight \: of \: the \:vessel=1\: m$

$\tt Volume \: of \: the \:vessel=0.0154\: m^3$

$\tt πr^2h = 0.0154$

$\tt r^2 = \dfrac{0.0154}{πh}$

$\tt r^2 = \dfrac{0.0154}{1× \frac{7}{22}}$

$\tt r^2 = 0.0049$

$\tt r = 0.07 \: m$

$\rm TSA_{Cylinder} = 2πr(r+h)$

$\tt : \implies 2× \dfrac{22}{7} ×0.07(0.07+1)$

$\tt : \implies 0.44×1.07$

$\tt : \implies 0.4708 \: m^2$

$\rm 0.4708 \: m^2$ of metal sheet would be needed to make the vessel.