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.)

2.75 m²  

Step-by-step 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:

Thus, the change in the volume now is:

∴

dV = 2π × (25)² (0.0007)

where;

dr = 0.0007

dV = 2π × (25)² (0.0007)

dV = 2.75 m²  

sup

step-by-step explanation: