Question

Marina is comparing the surface area of two soda cans. Can A has a diameter of

and a height of
while can B has a diameter of
and a height of
.

Which can has a greater surface area, and by how much? Use
.

has a greater surface area by

.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare the surface areas of the two soda cans, we first need to calculate the surface area of each can.

The formula for the surface area of a cylinder is:

Surface Area = 2πr^2 + 2πrh

Where r is the radius of the base of the cylinder and h is the height of the cylinder.

For Can A:
Radius = / 2 =
Height =

Surface Area A = 2π(2.5)^2 + 2π(2.5)(5)
Surface Area A = 2π(6.25) + 2π(12.5)
Surface Area A = 12.5π + 25π
Surface Area A = 37.5π square units

For Can B:
Radius = / 2 =
Height =

Surface Area B = 2π(3)^2 + 2π(3)(4)
Surface Area B = 2π(9) + 2π(12)
Surface Area B = 18π + 24π
Surface Area B = 42π square units

Now we compare the surface areas:

Surface Area A = 37.5π
Surface Area B = 42π

Can B has a greater surface area than Can A by:

42π - 37.5π = 4.5π square units

So, Can B has a greater surface area by 4.5π square units.