3 Geometry Questions I'm Really Struggling With. Please Help! {4/30/18}

(1) Marisol is in a bathtub that is shaped like a rectangular prism, about 5 ft long, 2 ft wide, and 1 ft deep. She is drinking hot cocoa that is in a cylindrical mug about 3 in. wide and 4 in. tall. She wonders how many mugs of water it would take to fill her tub. Her reasoning, shown here, contains an error.

• The bathtub has a volume of about 17,280 in³, or about 1×10^4 in³.
• The mug has a volume of about 28 in³, or about 3×10^1 in³.
• \(\frac{1*10^4}{3*10^1}=\frac{1}{3}*10^3\) , so about 333 mugs of water would fill the bathtub.

What is Marisol's error?

A: The volume of the tub is not abut 17,280 in³.

B: The value 28 should have been rounded to 2×10^1

C: The volume of the mug is not 28 in³.

D: The value 17,280 should have been rounded to 2×10^4 .

 

(2) Natasha wants to use the Fermi process to estimate the number of pennies that would fill a toy chest. As part of the process, she needs to estimate the volume of the toy chest. She figures the toy chest is about 50 in. long, 20 in. wide, and 20 in. tall.

 

Which estimate best approximates the volume of the toy chest?

A: 2×10^3 in³

B: 2×10^4 in³

C: 2×10^5 in³

D: 2×10^6 in³

 

(3) Eduardo uses the Fermi process and the following estimates to determine how many paperback books would fill the community pool he visits.

• A paperback book is about ​ 1/2 ​ ft long, ​ 1/5 ​ ft wide, and ​ 1/5 ​ ft thick.
• The swimming pool is about 40 ft long, 30 ft wide, and 5 ft deep.

Which equation could he have written?

A: \( \frac{6*10^3}{2*10^-2}=3*10^5\)

B: \( \frac{6*10^3}{2*10^-2}=3*10^1\)

C: \( \frac{6*10^4}{2*10^-2}=3*10^6\)

D: \( \frac{6*10^4}{2*10^-2}=3*10^2\)

 

 

Thank You!!!!