Important conversion between m square and cm square :
1 m = 100 cm
Take square on both sides
1 m^{2} = (100)^{2} cm^{2}
1 m^{2} = 10000 cm^{2}
1 cm = 1/100 m
Take square on both sides.
1 cm^{2} = (1/100)^{2} m^{2}
1 cm^{2} = 1/10000 m^{2}
Problem 1 :
Convert 3 m^{2} into cm^{2}
Solution :
Here, we convert bigger unit into smaller unit. So we have to multiply.
1 m^{2} = 10,000 cm^{2}
3 m^{2} = 3 × 10000
= 30000 cm^{2}
So, 3 m^{2} is equal to 30,000 cm^{2}.
Problem 2 :
Convert 72.5 m^{2} into cm^{2}
Solution :
Here, we convert bigger unit into smaller unit. So we have to multiply.
1 m^{2} = 10,000 cm^{2}
72.5 m^{2} = 72.5 × 10000
= 725000 cm^{2}
So, 72.5 m^{2} is equal to 725000 cm^{2}.
Problem 3 :
Convert 20000 cm^{2} into m^{2}
Solution :
Here, we convert smaller unit into bigger unit. So we have to divide.
1 cm^{2} = (1/10,000) m^{2}
20000 cm^{2} = (20000/10000) m^{2}
= 2 m^{2}
So, 20000 cm^{2} is equal to 2 m^{2}.
Problem 4 :
Convert 23000000 cm^{2} into m^{2}
Solution :
Here, we convert smaller unit into bigger unit. So we have to divide.
1 cm^{2} = (1/10,000) m^{2}
23000000 cm^{2} = (23000000/10000) m^{2}
= 2300 m^{2}
So, 23000000 cm^{2} is equal to 2300 m^{2}.
Problem 5 :
Convert 0.2 m^{2} into cm^{2}
Solution :
Here, we convert bigger unit into smaller unit. So we have to multiply.
1 m^{2} = 10,000 cm^{2}
0.2 m^{2} = 0.2 × 10000
= 2000 cm^{2}
So, 0.2 m^{2} is equal to 2000 cm^{2}.
Problem 6 :
Convert 552 cm^{2} into m^{2}
Solution :
Here, we convert smaller unit into bigger unit. So we have to divide.
1 cm^{2} = (1/10,000) m^{2}
552 cm^{2} = (552/10000) m^{2}
= 0.0552 m^{2}
So, 552 cm^{2} is equal to 0.0552 m^{2}.
Problem 7 :
Convert 8 m^{3} into cm^{3}
Solution :
Here, we convert bigger unit into smaller unit. So we have to multiply.
1 m^{3} = 10,00000 cm^{3}
8 m^{3} = 8 × 1000000
= 8000000 cm^{3}
So, 8 m^{3} is equal to 8000000 cm^{3}.
Problem 8 :
The area of one face of a cube is 36 cm^{2}. 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 cm^{2}.
(a) Let x be the length of the cube.
v = x^{3 }
36 = x^{3}
Taking cube root on each sides.
∛36 = ∛x^{3}
x = ∛36
So, the length of the cube is ∛36 cm.
(b) The total surface area of the cube = 6a^{2}
6a^{2} = 36
a^{2} = 36/6
a^{2} = 6
Taking square root on each sides.
√a^{2} = √6
a = √6
(c) The volume of the cube = a^{3}
= √6 × √6 × √6
= 6√6
= 6 × 2.45
= 14.7
So, volume of the cube is 14.7 cm^{3}.
Problem 9 :
The total surface area of a cube is 294 cm^{2}. 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 cm^{2}.
(a) The total surface area of the cube = 6a^{2}
6a^{2} = 294
a^{2} = 294/6
a^{2} = 49
a = 7 cm
So, area of one face of the cube is 7cm.
(b) Let x be the length of the cube.
v = x^{3}
294 = x^{3}
Taking cube root on each sides.
∛294 = ∛x^{3}
x = ∛294
(c) The volume of the cube = a^{3}
= 7 × 7 × 7
= 343
So, volume of the cube is 343 cm^{3}.
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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM