The volume of a cone is 316in^3. What is the volume of a similar cone that is larger by a scale of 3?
316/1 = x/3
cross multiply
316*3 = x
948 = x
x = 948 similar cone volume
316x3^3
316x9
=2,844in^3
To find the volume of a similar cone that is larger by a scale of 3, we can use the concept of similar shapes.
The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, π is pi (approximately 3.14159), r is the radius of the base of the cone, and h is the height of the cone.
Let's denote the volume of the original cone as V1 and the volume of the larger cone as V2. We have the following relation between the two cones:
V1 / V2 = (r1 / r2)^2 * (h1 / h2)
We are given the volume of the original cone, V1 = 316 in^3. Since the volumes are directly proportional to the cube of the corresponding lengths, we can set up the following equation:
316 / V2 = (r1 / r2)^2 * (h1 / h2)
Since we are given that the larger cone is scaled by a factor of 3, we can say that r2 = 3 * r1 and h2 = 3 * h1. Plugging these values and simplifying the equation, we get:
316 / V2 = (r1 / (3 * r1))^2 * (h1 / (3 * h1))
316 / V2 = (1/9) * (1/3)
Simplifying further:
316 / V2 = 1/27
Cross-multiplying the equation, we find:
V2 = 316 * 27
V2 = 8,532 in^3
Therefore, the volume of the similar cone that is larger by a scale of 3 is 8,532 in^3.