Question

trina is using 2 cylindrical glasses in an experiment. glass a measures 8 centimeters in diameter and 18 centimeters tall. glass b measures 10 centimeters in diameter and 13 centimeters tall. which one can hold more liquid? how much more? use 3.14 for π. glass __ can hold __ more cubic centimeters of liquid. enter letter a or b in the first box. enter the answer to the nearest hundredth in the second box.

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. The radius is half of the diameter, so \( r=\frac{d}{2} \).

Step2: Calculate the volume of Glass A

For Glass A:

• Diameter \( d_A = 8 \) cm, so radius \( r_A=\frac{8}{2}=4 \) cm.
• Height \( h_A = 18 \) cm.
• Using \( \pi = 3.14 \), the volume \( V_A = 3.14\times(4)^2\times18 \)
• First, calculate \( 4^2 = 16 \)
• Then, \( 3.14\times16 = 50.24 \)
• Finally, \( 50.24\times18 = 904.32 \) cubic centimeters.

Step3: Calculate the volume of Glass B

For Glass B:

• Diameter \( d_B = 10 \) cm, so radius \( r_B=\frac{10}{2}=5 \) cm.
• Height \( h_B = 13 \) cm.
• Using \( \pi = 3.14 \), the volume \( V_B = 3.14\times(5)^2\times13 \)
• First, calculate \( 5^2 = 25 \)
• Then, \( 3.14\times25 = 78.5 \)
• Finally, \( 78.5\times13 = 1020.5 \) cubic centimeters.

Step4: Compare the volumes and find the difference

• Compare \( V_A = 904.32 \) and \( V_B = 1020.5 \). Since \( 1020.5>904.32 \), Glass B holds more liquid.
• The difference in volume is \( V_B - V_A = 1020.5 - 904.32 = 116.18 \) cubic centimeters.

Answer:

First box: B
Second box: 116.18