# CONVERSION BETWEEN M SQUARE AND CM SQUARE

Important conversion between m square and cm square :

1 m = 100 cm

Take square on both sides

1 m2 = (100)2 cm2

1 m2 = 10000 cm2

1 cm = 1/100 m

Take square on both sides.

1 cm2 = (1/100)2 m2

1 cm2 = 1/10000 m2

Problem 1 :

Convert 3 m2 into cm2

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

1 m2 = 10,000 cm2

3 m2 = 3 × 10000

= 30000 cm2

So, 3 m2 is equal to 30,000 cm2.

Problem 2 :

Convert 72.5 m2 into cm2

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

1 m2 = 10,000 cm2

72.5 m2 = 72.5 × 10000

= 725000 cm2

So, 72.5 m2 is equal to 725000 cm2.

Problem 3 :

Convert 20000 cm2 into m2

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

1 cm2 = (1/10,000) m2

20000 cm2 = (20000/10000) m2

= 2 m2

So, 20000 cm2 is equal to 2 m2.

Problem 4 :

Convert 23000000 cm2 into m2

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

1 cm2 = (1/10,000) m2

23000000 cm2 = (23000000/10000) m2

= 2300 m2

So, 23000000 cm2 is equal to 2300 m2.

Problem 5 :

Convert 0.2 m2 into cm2

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

1 m2 = 10,000 cm2

0.2 m2 = 0.2 × 10000

= 2000 cm2

So, 0.2 m2 is equal to 2000 cm2.

Problem 6 :

Convert 552 cm2 into m2

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

1 cm2 = (1/10,000) m2

552 cm2 = (552/10000) m2

= 0.0552 m2

So, 552 cm2 is equal to 0.0552 m2.

Problem 7 :

Convert 8 m3 into cm3

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

1 m3 = 10,00000 cm3

8 m3 = 8 × 1000000

= 8000000 cm3

So, 8 m3 is equal to 8000000 cm3.

Problem 8 :

The area of one face of a cube is 36 cm2. Find

(a)  The length of the cube

(b)  The total surface area of the cube

(c)  The volume of the cube

Solution :

Area of one face of a cube is 36 cm2.

(a) Let x be the length of the cube.

v = x

36 = x3

Taking cube root on each sides.

∛36 = ∛x3

x = ∛36

So, the length of the cube is ∛36 cm.

(b)  The total surface area of the cube = 6a2

6a2 = 36

a2 = 36/6

a2 = 6

Taking square root on each sides.

√a2 = √6

a = √6

(c)  The volume of the cube = a3

= √6 × √6 × √6

= 6√6

= 6 × 2.45

= 14.7

So, volume of the cube is 14.7 cm3.

Problem 9 :

The total surface area of a cube is 294 cm2. Find :

(a)  The area of one face of the cube

(b)  The length of the cube

(c)  The volume of the cube

Solution :

Total surface area of a cube is 294 cm2.

(a) The total surface area of the cube = 6a2

6a2 = 294

a2 = 294/6

a2 = 49

a = 7 cm

So, area of one face of the cube is 7cm.

(b) Let x be the length of the cube.

v = x3

294 = x3

Taking cube root on each sides.

∛294 = ∛x3

x = ∛294

(c)  The volume of the cube = a3

= 7 × 7 × 7

= 343

So, volume of the cube is 343 cm3.

Problem 10 :

On an architect’s drawing of the floor plan for a house, 1 inch represents 3 feet. If a room is represented on the floor plan by a rectangle that has sides of lengths 3.5 inches and 5 inches, what is the actual floor area of the room, in square feet?

A) 17.5       B) 51.0      C) 52.5        D) 157.5

Solution :

To solve this problem, we have two ways.

Method 1 :

Converting the dimensions of the rectangle from inches to feet and find the area.

Length = 3.5 inches

1 inch = 3 feet

Length in feet = 3.5 x 3 ==> 10.5 feet

Width = 5 inches

Width in feet = 5 x 3 ==> 15 feet

Area of the floor = 10.5 x 15

= 157.5 square feet

Method 2 :

Find the area of the rectangle and convert the square inches to square feet.

Area of the floor = 3.5 x 5

= 17.5 square inches

1 inch = 3 feet

Take square on both sides.

1 square inches = 9 square feet

= 17.5 x 9

= 157.5 square feet

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