Question
The volume of a spherical bowling ball is 322 cubic inches. The formula for the volume of a sphere is V = fr'.
What is the approximate diameter of the bowling ball rounded to the nearest tenth of an inch? (Use 3.14 as an approximation of pi.)
• 4.3 inches
• 8.2 inches
• 8.5 inches
• 8.8 inches
What is the approximate diameter of the bowling ball rounded to the nearest tenth of an inch? (Use 3.14 as an approximation of pi.)
• 4.3 inches
• 8.2 inches
• 8.5 inches
• 8.8 inches
Answers
GPT 3.5
The given formula for the volume of a sphere is incorrect. The correct formula is V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Since the volume of the bowling ball is given as 322 cubic inches, we can equate this to the formula:
322 = (4/3) * π * r^3
To find the radius, we can rearrange the equation:
r^3 = (3/4 * 322) / π
r^3 = 241.5 / 3.14
r^3 ≈ 76.84
Taking the cube root of both sides, we find the radius:
r ≈ ∛(76.84) ≈ 4.3 inches (rounded to one decimal place)
The diameter of the bowling ball is twice the radius, so the approximate diameter is:
Diameter ≈ 2 * r ≈ 2 * 4.3 ≈ 8.6 inches
Rounded to the nearest tenth of an inch, the approximate diameter of the bowling ball is 8.6 inches. None of the provided answer choices are correct.
Since the volume of the bowling ball is given as 322 cubic inches, we can equate this to the formula:
322 = (4/3) * π * r^3
To find the radius, we can rearrange the equation:
r^3 = (3/4 * 322) / π
r^3 = 241.5 / 3.14
r^3 ≈ 76.84
Taking the cube root of both sides, we find the radius:
r ≈ ∛(76.84) ≈ 4.3 inches (rounded to one decimal place)
The diameter of the bowling ball is twice the radius, so the approximate diameter is:
Diameter ≈ 2 * r ≈ 2 * 4.3 ≈ 8.6 inches
Rounded to the nearest tenth of an inch, the approximate diameter of the bowling ball is 8.6 inches. None of the provided answer choices are correct.