A collar of Styrofoam is made to insulate a pipe. Find its volume . The large R is to the outer rim. The small radius r is to the edge of the insulation. Use 3.14 for pi. r = 5 in. R = 8 in. h = 25 in. use pi
14 million cubic inches seems a bit high...
oops i put use pi twice
V=hp(R^2-r^2)
V=1515(3.14)(77^2-55^2) in^3
V≈13814618.4 in^3
Hope this helps!
π * (R^2 - r^2) * 25 = ? in^3
To find the volume of the collar of Styrofoam, we can think of it as being made up of two cylinders and a frustum (the shape formed by cutting the top of a cone).
First, let's calculate the volume of the outer cylinder. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the radius is R = 8 in and the height is h = 25 in. Plugging in these values, we get:
V_outer_cylinder = π * (8 in)^2 * 25 in
V_outer_cylinder = π * 64 in^2 * 25 in
V_outer_cylinder = 1600π in^3
Next, let's calculate the volume of the inner cylinder. The radius of the inner cylinder is r = 5 in, and the height is still h = 25 in. Using the same formula, we get:
V_inner_cylinder = π * (5 in)^2 * 25 in
V_inner_cylinder = π * 25 in^2 * 25 in
V_inner_cylinder = 625π in^3
Finally, let's calculate the volume of the frustum. The formula for the volume of a frustum is V = (1/3)πh(a^2 + ab + b^2), where h is the height, and a and b are the radii of the ends. In this case, a is the radius of the outer end (R = 8 in) and b is the radius of the inner end (r = 5 in). Plugging in these values, we get:
V_frustum = (1/3)π * 25 in * (8^2 + 8*5 + 5^2)
V_frustum = (1/3)π * 25 in * (64 + 40 + 25)
V_frustum = (1/3)π * 25 in * 129
V_frustum = 43 * 25π in^3
V_frustum = 1075π in^3
Now, we can find the total volume of the collar of Styrofoam by adding together the volumes of the outer cylinder, inner cylinder, and frustum:
V_total = V_outer_cylinder + V_inner_cylinder + V_frustum
V_total = 1600π in^3 + 625π in^3 + 1075π in^3
V_total = 3300π in^3
Therefore, the volume of the collar of Styrofoam is 3300π cubic inches.