Question

PLEASE ANSWER 80 POINTS! PLEASE!

Riley’s mother, Ms. Cooper, owns Cooper’s Storage and Shipping Company. Ms. Cooper took Riley with her to work for the day to show Riley the different jobs the company does.
1. Riley noticed an aquarium in his mother’s office. The aquarium has the dimensions 16 in. by 8.5 in. by 10.5 in. The formula for volume is: V = l x w x h  
(a) Riley noticed that the aquarium was three-fourths full of water. How many more cubic inches of water would be required to fill the tank? Show your work.

(b) Another aquarium in the building has dimensions that are each triple the dimensions of the aquarium in Riley’s mother’s office. Riley thought that the volume would also triple. Is Riley correct? How many times greater is the volume of the larger aquarium than the volume of the smaller one? Show your work and explain your reasoning.

(c) Riley also thought that the surface area would triple. Is Riley correct? How many times greater is the surface area of the larger aquarium than the surface area of the smaller one? Show your work and explain your reasoning.

Here is one more

Riley finds out that Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. Some of the supplies are packed inside a cube-shaped box with side lengths of 4 1/2
in.
These boxes are then packed into a shipping box with dimensions of 18 in. 9 in. 4 1/2 in. 

(a) How many boxes of office supplies can be packed into the larger box for shipping? Show your work.

(b) Sometimes the shipping boxes are protected with an outer covering because of weather. Draw a net of the shipping box. Use the net to find the surface area of the shipping box to help decide how much outer covering will be needed to protect one box. Show your work.

Answer 1

See the attached picture for the complete answers to both questions:

Question A asked how much more water was required to fill the tank, so you need to calculate the full volume, then subtract 3/4 of the volume.

Question B, volume is cubed, so you need to cube the scale factor of 3. 3^3 = 27, so the larger tank is 27 times more.

Question C) Area is squared so you need to square the scale factor. Surface area would be 9 times more. 3^2 = 9

For the 2nd question, calculate the volume of each box and divide to find the number of boxes.

Then see the picture for total surface area for part B.