Aladdin found a cave filled with boxes of gold, measuring 2 inches × 2 inches × 2 inches, and boxes of silver, measuring 1 inch × 1 inch × 1 inch. however, aladdin brought only one box measuring 6 inches × 6 inches × 7 inches with him. he filled it with as many boxes of gold as would fit, then put as many boxes of silver as would fit in the remaining space. how many boxes of treasure did aladdin take?

Aladdin took 32 boxes of treasure.

Step-by-step explanation:

The dimensions of the box Aladdin brought are 6 inch × 6 inch × 7 inch.

Since, the volume of the box = Length × Width × Height.

So, the volume of the Aladdin's box = 6 × 6 × 7 = 252 inch³

Now, the dimensions of the gold box are 2 inch × 2 inch × 2 inch.

So, the volume of the gold box = 2 × 2 × 2 = 8 inch³

Thus, the number of gold boxes which can fit inside Aladdin's box = = 31 boxes

Also, as the dimensions of the silver box are 1 inch × 1 inch × 1 inch.

So, the volume of the silver box = 1 × 1 × 1 = 1 inch³

Then, the number of silver boxes which can fit inside Aladdin's box is 1.

Hence, Aladdin took 31 + 1 = 32 boxes of treasure.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

56

step-by-step explanation: