Surrounding area and total area of a cube

**Lesson 1:** Calculate the perimeter and total area of a cube with side a given below:

a = 3.5 cm; a = 1.5m; a = 2.4dm

**Solution**

With a = 3.5 cm, then

S_{xq} = 3.5 x 3.5 x 4 = 49 (cm^{2})

S_{city }= 3.5 x 3.5 x 6 = 73.5 (cm^{2})

For a = 1.5 cm, then

S_{xq} = 1.5 x 1.5 x 4 = 9 (m^{2})

S_{city} = 1.5 x 1.5 x 6 = 13.50 (m^{2})

With a = 2.4dm, then

Sxq = 2.4 x 2.4 x 4 = 23.04 (dm^{2})

Scity = 2.4 x 2.4 x 6 = 34.56 (dm^{2})

**Lesson 2: **The small cube has a side of 8cm, the big cube has a side 4 times longer than the side of the small cube. Ask:

a. How many times larger is the surrounding area of the small figure?

b. How many times the total area of the small figure is the total area of the large figure?

**Solution**

a.

The side of the large cube is: 8 x 4 = 32 (cm)

S_{xq} small cube is: 8 x 8 x 4 = 256 (cm2)

S_{xq} big cube is: 32 x 32 x 4 = 4096 (cm2)

So WILL_{xq} cube is equal to \(\frac{{2304}}{{256}} = 16\) (times) S_{xq} small cube.

b.

Scity the small cube is: 8 x 8 x 6 = 384 (cm^{2})

Stp large cube is: 32 x 32 x 6 = 6144 (cm^{2})

So WILLcity large cube is equal to \(\frac{{2304}}{{256}} = \frac{1}{{16}}\) (times) Stp large cube.

**Lesson 3: **Fill in the blanks in the following table:

Side of the cube | 5cm | ||

Area of one side | 36m^{2} |
||

Total area | 294dm^{2} |

**Solution**

Side of the cube | 5cm | 6m |
7dm |

Area of one side | 25cm^{2} |
36m^{2} |
49dm2 |

Total area | 150cm^{2} |
216m^{2} |
294dm^{2} |

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