a box whose volume is 80cubic cm has
length,width and height in the ratio
1:2:5 if each of the length,width,height is increased by 2cm how many cubic centimeters will the volume be increased?/
original box
x (2x)(5x) = 80
x^3 = 8
so
x = 2
2x = 4
5x = 10
now new box
4 * 6 * 12 = 288 cm^3
increase = 288 - 80 = 208
Well, it sounds like this box is undergoing a growth spurt! So, if we increase each side by 2 cm, the new dimensions will become 3 cm, 4 cm, and 7 cm. Now let's calculate the new volume:
Volume = length x width x height
Initial Volume = 1 cm x 2 cm x 5 cm = 10 cm³
New Volume = 3 cm x 4 cm x 7 cm = 84 cm³
To find out the increase in volume, we subtract the initial volume from the new volume:
Increase in Volume = New Volume - Initial Volume
Increase in Volume = 84 cm³ - 10 cm³ = 74 cm³
So, the volume will be increased by 74 cubic centimeters. This box is really growing up!
The ratio between the length, width, and height of the box is 1:2:5. Let's represent the length, width, and height as L, W, and H respectively.
From the given information, we can write the following equations:
L : W : H = 1 : 2 : 5
L = x
W = 2x
H = 5x
The volume of the box is given by V = L * W * H = x * 2x * 5x = 10x^3
Given that the volume of the box is 80 cubic cm, we can solve for x:
10x^3 = 80
x^3 = 8
x = 2
So, the original dimensions of the box are L = 2 cm, W = 4 cm, and H = 10 cm.
If each of the length, width, and height is increased by 2 cm, the new dimensions of the box will be:
L + 2 = 2 + 2 = 4 cm
W + 2 = 4 + 2 = 6 cm
H + 2 = 10 + 2 = 12 cm
The new volume of the box can be calculated as V' = (L + 2) * (W + 2) * (H + 2) = 4 * 6 * 12 = 288 cubic cm
To find the increase in volume, we subtract the original volume from the new volume:
Increase in volume = V' - V = 288 - 80 = 208 cubic cm
Therefore, the volume will be increased by 208 cubic centimeters.
To find out how many cubic centimeters the volume will be increased by, we first need to calculate the initial volume of the box and the volume after the dimensions are increased.
Let's first determine the dimensions of the box. The ratio of the length, width, and height is given as 1:2:5, which means the length is 1x, the width is 2x, and the height is 5x, where x is a constant.
The initial volume of the box is calculated as the product of the length, width, and height:
Initial Volume = length x width x height
= (1x) x (2x) x (5x)
= 10x^3 cubic cm
Given that the initial volume is 80 cubic cm, we can equate:
10x^3 = 80
Next, we solve this equation to find the value of x:
x^3 = 80/10
x^3 = 8
x = 2
Now that we have found the value of x, we can calculate the dimensions of the box:
Length = 1x = 1(2) = 2 cm
Width = 2x = 2(2) = 4 cm
Height = 5x = 5(2) = 10 cm
The initial volume of the box is 10x^3 = 10(2^3) = 80 cubic cm.
To find the volume after increasing each dimension by 2 cm, we add 2 to each dimension:
New Length = 2 cm + 2 cm = 4 cm
New Width = 4 cm + 2 cm = 6 cm
New Height = 10 cm + 2 cm = 12 cm
The new volume of the box is calculated as the product of the new length, width, and height:
New Volume = New Length x New Width x New Height
= 4 cm x 6 cm x 12 cm
= 288 cubic cm
Finally, we can determine the increase in volume:
Increase in Volume = New Volume - Initial Volume
= 288 cubic cm - 80 cubic cm
= 208 cubic cm
Therefore, the volume will be increased by 208 cubic centimeters.