a cone has a volume of 134.4 cubic centimeters. suppose you reduce the dimensions by 1/2 their current value. What's the value of the resulting change?
If the linear dimensions are reduced to (1/2), the volume is reduced to (1/2)³ of the original value, or
134.4/8 cubic centimetres.
The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width?
To find the resulting change in the volume of the cone when its dimensions are reduced by half, we need to understand the relationship between the volume of a cone and its dimensions.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cone, and h is the height of the cone.
Let's assume the current dimensions of the cone are represented by r1 for the radius and h1 for the height. Therefore, the original volume V1 is given as V1 = (1/3) * π * r1^2 * h1.
When the dimensions are reduced by half, the new dimensions become r2 = r1/2 and h2 = h1/2. So, the new volume V2 is given as V2 = (1/3) * π * (r1/2)^2 * (h1/2).
To find the resulting change, we can calculate the ratio of the new volume to the original volume:
Resulting Change = V2 / V1
= ((1/3) * π * (r1/2)^2 * (h1/2)) / ((1/3) * π * r1^2 * h1)
= (1/8) * (r1^2 * h1) / (r1^2 * h1)
= 1/8
Therefore, the resulting change is 1/8, which can also be expressed as 0.125 or 12.5%.