Question

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 50 m. (Round your answer to two decimal places.)

Answer 1

2.75 m²

Explanation:

From the information given:

the thickness of the paint = 0.07 cm = (0.07/100) m

= 0.0007 m thick

the diameter hemispherical dome = 50 m

∴

radius of the dome = 50m /2 = 25 m

The volume of a hemispherical dome is expressed as:

`V = (2)/(3)\pi r^3`

Thus, the change in the volume now is:

`(dV)/(dr) = (2)/(3)\pi *3 r^2`

`{dV} = (2)/(3)\pi *3 r^2 (dr)`

`{dV} = 2 \pi r^2 (dr)`

∴

dV = 2π × (25)² (0.0007)

where;

dr = 0.0007

dV = 2π × (25)² (0.0007)

dV = 2.75 m²