Exercise 77 Page 478

We are told that the volume of a cube is 50 cubic centimeters, and we want to find the length of its sides. Let's visualize the situation by drawing a cube and letting s be the length of its sides.

When we find the volume of a prism, we multiply its three side measurements — the length, the width, and the height &mdash. In a cube, these three dimensions all happen to be the same. Recall that multiplying a number by itself three times is equal to raising the number to the power of 3. V= s* s* s ⇔ V= s^3 Since we already know that the volume is 50 cubic centimeters, let's substitute this value for V in the formula and solve for s.

V=s^3

Substitute

V= 50

50=s^3

▼

Solve for s

RadicalEqn

sqrt(LHS)=sqrt(RHS)

sqrt(50)=sqrt(s^3)

RootPowToNumber

sqrt(a^3)=a

sqrt(50)=s

CalcRoot

Calculate root

3.684031... =s

RoundDec

Round to 1 decimal place(s)

3.7≈ s

RearrangeEqn

Rearrange equation

s ≈ 3.7

The length of each side of a cube with a volume of 50 cubic centimeters is sqrt(50), or about 3.7, centimeters.