The capacity of a closed cylindrical vessel of height 1 metre is 15.4 litres.how many square meters of metal sheet would be needed to make it?

Answer 1

To find the surface area of the closed cylindrical vessel, we first need to determine its radius. The volume ( V ) of a cylinder is given by ( V = \pi r^2 h ). Given that the volume is 15.4 liters (or 0.0154 cubic meters) and the height ( h ) is 1 meter, we can rearrange the formula to find the radius ( r ).

Calculating, we have:

[ 0.0154 = \pi r^2 \cdot 1 \implies r^2 = \frac{0.0154}{\pi} \implies r \approx 0.0695 \text{ m} ]

The surface area ( A ) of a closed cylinder is given by ( A = 2\pi r(h + r) ). Plugging in the values:

[ A \approx 2\pi(0.0695)(1 + 0.0695) \approx 0.439 \text{ square meters} ]

Thus, approximately 0.439 square meters of metal sheet would be needed to make the closed cylindrical vessel.