Bob bought a glass pyramid from a gift store. The pyramid, with a height of 5 cm and a square base of side 6 cm, was packed in a box shaped as a cube of side 7 cm. The empty space in the box was packed with paper tissue.

How many cubic centimeters of the box were stuffed with paper tissue?

A 283 cubic centimeters
B 293 cubic centimeters
C 313 cubic centimeters
D 343 cubic centimeters

Question

Bob bought a glass pyramid from a gift store. The pyramid, with a height of 5 cm and a square base of side 6 cm, was packed in a box shaped as a cube of side 7 cm. The empty space in the box was packed with paper tissue. 
 
How many cubic centimeters of the box were stuffed with paper tissue?

A		283 cubic centimeters
B		293 cubic centimeters
C		313 cubic centimeters
D		343 cubic centimeters

anonymous · Answer

A. 283 cm^3

anonymous · Answer

How did you get that though?

anonymous · Answer

The cube has a volume s^3 =7^3=343. The pyramid had a volume of BH/3 where B is the area of the base and h is the height. B is 6*6=36, h=5 so V=60
Vtp=Vc-Vp Vtp=343-60=283 cm^3

anonymous · Answer

What about this question? I got the answer 8 times is greater (B) but I keep second guessing it. 

A floor has two square-shaped designs. The area of the second square-shaped design is sixteen times greater than the area of the first square-shaped design. Which statement gives the correct relationship between the lengths of the sides of the two squares?

A		The length of the side of the second square is 2 times greater than the length of the side of the first square.

B		The length of the side of the second square is 8 times greater than the length of the side of the first square.
 
C		The length of the side of the second square is 16 times greater than the length of the side of the first square.
 
D	The length of the side of the second square is 4 times greater than the length of the side of the first square.

anonymous · Answer

D. The length of the side of the second square is 4 times greater than the length of the side of the first square.

anonymous · Answer

Wait for one sec, double checking.....

anonymous · Answer

I got D. as the answer again.

anonymous · Answer

ok and how did you get that?

anonymous · Answer

The ratio of the sides would be the square root of of the ratios of the areas. Square root of 16 = 4.  4*4=16

anonymous · Answer

I had to redo it but I'm pretty sure that's right.

anonymous · Answer

ok thanks. I must have done something wrong :)

anonymous · Answer

No problem. I do that all the time to :P

anonymous · Answer

Wish you luck on your test. :)