Answer:
64
Step-by-step explanation:
Volume of a cube is:
V = s³
When s = 8 in:
V = (8 in)³ = 512 in³
When s is doubled (s = 16 in):
V = (16 in)³ = 4096 in³
Now we can write a proportion:
8 mugs / 512 in³ = x mugs / 4096 in³
x = 64
The maximum number of mugs that the larger box can hold is:
64
The edge length of box is: 8 inches.
This means that the volume of box is: 8×8×8=512 cubic inches.
Also, the number of mugs a box of edge length 8 in. can hold is: 8
Hence, volume of 1 mug= Volume of box/Number of mugs
Volume of 1 mug= 512/8=64 cubic inches
Now, if the dimension of the box is doubled.
This means that the Volume of new box= 8×Volume of old box
Volume of new box=8×512=4096 cubic inches
Let n be the number of mugs that the new box can hold.
Volume of new box=n×Volume of 1 mug
⇒ 4096=n×64
⇒ n=4096/64
⇒ n=64
Hence, the answer is:
64
