Question

a soup company is looking at two designs for a new can. can a has a diameter of 8 centimeters and a height of 15 centimeters. can b has a diameter of 10 centimeters and a height of 12 centimeters. how much greater is the volume of can b than can a? use 3.14 for π and give the difference to the nearest cubic centimeter. to the nearest cubic centimeter, the volume of can b is ______ cubic centimeters greater than can a. the solution is

Explanation:

Answer:

First, recall the formula for the volume of a cylinder, \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

For Can A:

• Diameter = 8 cm, so radius \( r_A = \frac{8}{2} = 4 \) cm.
• Height \( h_A = 15 \) cm.
• Volume \( V_A = 3.14 \times 4^2 \times 15 = 3.14 \times 16 \times 15 = 753.6 \) cubic centimeters.

For Can B:

• Diameter = 10 cm, so radius \( r_B = \frac{10}{2} = 5 \) cm.
• Height \( h_B = 12 \) cm.
• Volume \( V_B = 3.14 \times 5^2 \times 12 = 3.14 \times 25 \times 12 = 942 \) cubic centimeters.

Now, find the difference in volume: \( V_B - V_A = 942 - 753.6 = 188.4 \). Rounding to the nearest cubic centimeter, we get 188.

So the volume of Can B is \(\boxed{188}\) cubic centimeters greater than Can A.