The circumference of a bowling ball is about 27 inches. Find its volume to the nearest tenth.
c = 2πr, so r = C/2π
v = 4/3 π r^3 = 4/3 π (C/2π)^3
= 4/3 π C^3/8π^3
= 1/6 C^3/π^2
To find the volume of a bowling ball, we need to know its radius. The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
Given that the circumference of the bowling ball is 27 inches, we can solve for the radius:
27 = 2πr
Dividing both sides by 2π, we get:
r = 27 / (2π) = 27 / 6.28 ≈ 4.310
Now, we can use the formula for the volume of a sphere:
V = (4/3)πr³
Substituting the value of the radius we just found, we have:
V = (4/3)π(4.310)³ ≈ 323.057
Rounding to the nearest tenth, the volume of the bowling ball is approximately 323.1 cubic inches.
To find the volume of a bowling ball, we need to know either its radius or its diameter. The formula for the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.
However, we are given the circumference of the bowling ball, not its radius.
To find the radius from the circumference, we can use the formula:
C = 2 * π * r
Rearranging the formula, we have:
r = C / (2 * π)
Substituting the given circumference of 27 inches into the formula, we get:
r = 27 / (2 * π) ≈ 4.288
Now that we have the radius, we can find the volume using the formula for the volume of a sphere:
V = (4/3) * π * (4.288)^3 ≈ 328.34
Therefore, the volume of the bowling ball is approximately 328.34 cubic inches, to the nearest tenth.