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Core Connections Geometry, 2013

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Core Connections Geometry, 2013 View details

3. Section 10.3

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Exercise 118 Page 633

Do you remember the formulas for volume and surface area?

Volume: 1 000 000 cm^3
Surface Area: 60 000cm^2

Practice makes perfect

Before calculating the volume and the surface area of the cube, we should find its side length.

Side Length

We are given that the sum of side lengths of the cube is 1200cm. Since the cube has 12 side, to get the side length s, we should divide the sum by 12. 12s = 1200cm ⇔ s = 100cm

Volume

The volume of a cube with s side length can be calculated using the formula below. V= s^3 Since we found that s = 100cm, we can substitute this value into equation above to find the volume.

V= s^3

s= 100

V= 100^3

Calculate power

V = 1 000 000

The volume of the cube is 1 000 000 cm^3.

Surface area

To calculate the surface area of a cube, we can use the formula below. S= 6s^2 Let's substitute s =100cm again, to find the area.

S= 6s^2

s= 100

S = 6( 100)^2

Calculate power

S = 6(10 000)

Multiply

S = 60 000

The surface area is 60 000cm^2.

Subchapter links

10.3.1 The Fundamental Principle of Counting p.631-633

10.3.2 Permutations p.638-640

10.3.3 Combinations p.643-645

10.3.4 Categorizing Counting Problems p.649-650

10.3.5 Some Challenging Probability Problems p.658-660