Math Problem Statement

What is the volume of a sphere with a diameter of 27.3 in, rounded to the nearest tenth of a cubic inch?

Solution

To find the volume of a sphere, you can use the formula:

V=43πr3V = \frac{4}{3} \pi r^3

where rr is the radius of the sphere.

Given that the diameter of the sphere is 27.3 inches, the radius rr is half of the diameter:

r=27.32=13.65 inchesr = \frac{27.3}{2} = 13.65 \text{ inches}

Now, substitute the radius into the volume formula:

V=43π(13.65)3V = \frac{4}{3} \pi (13.65)^3

Calculating this:

V43×3.1416×2542.022V \approx \frac{4}{3} \times 3.1416 \times 2542.022

V10664.205 cubic inchesV \approx 10664.205 \text{ cubic inches}

Rounding to the nearest tenth:

V10664.2 cubic inchesV \approx 10664.2 \text{ cubic inches}

So, the volume of the sphere is approximately 10,664.2 cubic inches.

Would you like further details or have any questions? Here are some related questions you might find interesting:

  1. How does the volume change if the diameter is doubled?
  2. What is the surface area of the same sphere?
  3. How do you derive the formula for the volume of a sphere?
  4. What is the volume of a hemisphere with the same radius?
  5. How does the volume of a sphere compare to the volume of a cylinder with the same height and diameter?

Tip: Remember that the volume of a sphere grows rapidly as the radius increases, since it’s proportional to the cube of the radius.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a sphere

Formulas

Volume of a sphere: V = (4/3)πr^3

Theorems

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Suitable Grade Level

Grades 9-12