Question

A rectangular block of candy 10 inches by 10 inches by 5 inches is coated on all faces with a very thin layer of chocolate. The block of candy is then cut into cubes measuring 1 inch by 1 inch by 1 inch. What percent of the cubes have no chocolate on them

Answer 1

38.2% of the cubes are without chocolate coated.

Calculation

Given that,

The length ,l= 10 inch

The width ,b=10 inch

The height, h=5 inch

We know that the lateral surface area of the cuboid or rectangular block,

SA= 2(lh+lb+hb)

⇒ SA = 2( 10*5 +10*10+5*10)

⇒ SA =2*200=400 $inch^{3}$  

The volume of the cuboid,V= 10*10*5 =500 $inch^{3}$

The block of candy is then cut into another small cube 1 inch per side.

length,l=1 inch

width, b=1 inch

height,h=1 inch

So, the surface area of each small cube ,sa= 2(1+1+1) = 6 $inch^{3}$

Volume of each candy,v= 1*1*1=1 $inch^{3}$

So, the total number of candy= 500/1 =500 nos.

There is chocolate on each and every piece on the exterior inch. But those who are totally within do not.

A cube measuring 8 inches by 8 inches by 3 inches makes up the inside.

So, the total no of boxes that have no chocolate =8*8*3=192 boxes

So, the percentage = 192*100/500= 38.2 %

Therefore, it is concluded that 38.2% of cubes are without chocolate.

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