A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm

Mathematics

1 answer:

Sophie [7]1 year ago

7 0

The surface area of the cylinder is 5969.03 cm²

The internal volume is 23156.68 cm³

Given:

A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm

To Find
a) the surface area of the tank

We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.

So, the surface area of the cylinder is

$\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2$
= π×(100+1600+200)

= π×(1900)

= 5969.03 cm²

b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm

= $\frac{4}{3}\times \pi \times 9^3$ + $\pi\times 9^2\times 79$