Question

What is the percent increase in the surface area of the AAA battery to the AA battery? Round your answer to the nearest tenth of a percent.

Answer 1

101.1%

Explanation:

The two batteries are in the shape of cylinder.

The total surface area of a cylinder

SA = (2πr^2 + 2πrh ) =

For AAA battery

h = 0.8mm

r = 1.9 mm

SA = (2π(1.9)^2 + 2π × 1.9 × 0.8 )

SA = 22.68 + 9.55

SA = 32.23 mm^2

For AA battery

h = 1 mm

r = 2.75 mm

SA = (2π(2.75)^2 + 2π×2.75× 1 )

SA = 47.52 + 17.28

SA = 64.80 mm^2

Increase in SA = 64.80 - 32.23

Increase in SA = 32.57

% increase = increase in SA/AAA × 100

% increase in SA = 32.57/32.23 × 100

% increase in SA = 101.1%