CONVERSION BETWEEN M SQUARE AND CM SQUARE

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 = x³ 

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