Question

A cylinder tank has a radius of 7.5 feet and an altitude of 14 feet. If a gallon of paint will cover 130 ft.² of surface how much paint is needed to put two coats of paint on the entire surface of the tank?

Answer 1

A cylinder tank has a radius of 7.5 feet and an altitude of 14 feet. If a gallon of paint will cover 130 ft.² of surface how much paint is needed to put two coats of paint on the entire surface of the tank?

Remember that

The surface area of a cylinder is equal to

`SA=2B+Ph`

where

B is the area of the circular nase

P is the circumference of the circular base

h is the height of the cylinder

so

Find out B

`B=\pi\cdot r^2`

we have

r=7.5 ft

pi=3.14

substitute

`\begin{gathered} B=3.14\cdot(7.5)^2 \\ B=176.625\text{ ft2} \end{gathered}`

Find out the circumference

`\begin{gathered} P=2\pi\cdot r^{} \\ P=2(3.14)\cdot7.5 \\ P=47.1\text{ ft} \end{gathered}`

the value of h=14 ft

therefore

SA=2(176.625)+47.1(14)

SA=1,012.65 ft2

Remember that s needed to put two coats of paint

Multiply the surface area by 2

1,012.65*2=2,025.3 ft2

1 gallon -------> 130 ft2

applying proportion

1/130=x/2,025.3

solve for x

x=2,025.3/130

x=15.6 gal

therefore

the answer is 16 gallon