The diameter, D, of a sphere is 15.8cm. Calculate the sphere’s volume, . Use the value 3.14 for ?, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The Correct Answer and Explanation is:
To calculate the volume of a sphere, we use the formula:V=43πr3V = \frac{4}{3} \pi r^3V=34πr3
Where:
- VVV is the volume,
- π\piπ is approximately 3.14,
- rrr is the radius of the sphere.
The problem provides the diameter of the sphere, D=15.8 cmD = 15.8 \, \text{cm}D=15.8cm, so we need to find the radius rrr. The radius is half the diameter:r=D2=15.82=7.9 cmr = \frac{D}{2} = \frac{15.8}{2} = 7.9 \, \text{cm}r=2D=215.8=7.9cm
Now, we substitute the radius and the value of π\piπ into the volume formula:V=43×3.14×(7.9)3V = \frac{4}{3} \times 3.14 \times (7.9)^3V=34×3.14×(7.9)3
First, we calculate r3r^3r3:7.93=7.9×7.9×7.9=493.0397.9^3 = 7.9 \times 7.9 \times 7.9 = 493.0397.93=7.9×7.9×7.9=493.039
Now, substitute r3=493.039r^3 = 493.039r3=493.039 into the volume formula:V=43×3.14×493.039V = \frac{4}{3} \times 3.14 \times 493.039V=34×3.14×493.039V=43×1545.218V = \frac{4}{3} \times 1545.218V=34×1545.218V=2060.291 cm3V = 2060.291 \, \text{cm}^3V=2060.291cm3
Finally, rounding to the nearest tenth:V≈2060.3 cm3V \approx 2060.3 \, \text{cm}^3V≈2060.3cm3
Conclusion:
The volume of the sphere is approximately 2060.3 cm³.
