Question

A solid is in the form of a cylinder with hemispherical ends the total height of solid is 19 cm and diameter of cylinder is 7 cm find the volume and surface area of solids

Answer 1

I am not sure about the answer

Answer 2

Answer:

The total volume of solid is 910.335 cm³ .

The total surface area of the solid is 571.48 cm² .

Step-by-step explanation:

Formula

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

$Volume\ of\ a\ hemisphere = \frac{2}{3} \pi r^{3}$

Where r is the radius and h is the height .

As given

A solid is in the form of a cylinder with hemispherical ends the total height of solid is 19 cm and diameter of cylinder is 7 cm .

$Radius = \frac{Diameter}{2}$

$Radius = \frac{7}{2}$

Radius = 3.5 cm

Thus

Total Volume = Volume of a cylinder  + 2 × Volume of a hemisphere

$Total\ Volume = 3.14\times 3.5\times 3.5\times 19 + 2\times \frac{2}{3}\times 3.14\times 3.5\times 3.5\times 3.5$

$Total\ Volume = 730.835+\frac{2\times 2\times 3.14\times 3.5\times 3.5\times 3.5}{3}$

$Total\ Volume = 730.835+\frac{538.51}{3}$

$Total\ Volume = 730.835+179.50$

Total volume = 910.335 cm³

Therefore the total volume of solid is 910.335 cm³ .

Formula

$Curved\ surface\ area\ of\ a\ cylinder = 2\pi r h$

$Curved\ surface\ area\ of\ a\ hemisphere = 2\pi r^{2}$

Where r is the radius .

Thus

Total surface area  = Area of a cylinder + 2 × Area of a hemisphere

                               = 2 × 3.14 × 3.5 × 19 + 2 × 2 × 3.14 × 3.5 × 3.5

                               = 417.62 + 153.86

                               = 571.48 cm²

Therefore the total surface area of the solid is 571.48 cm² .