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 = 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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM