Part a: The radius of the second sphere is 5 inches.
Part b: The volume of the second sphere is 523.33 in³
Part c; The radius of the third sphere is 1.875 inches.
Part d: The volume of the third sphere is 27.59 in³
Explanation:
Given that the radius of the sphere is 2.5 inches.
Part a: We need to determine the radius of the second sphere.
Given that the second sphere has twice the radius of the given sphere.
Radius of the second sphere = 2 × 2.5 = 5 inches
Thus, the radius of the second sphere is 5 inches.
Part b: we need to determine the volume of the second sphere.
The formula to find the volume of the sphere is given by
![V=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%20r%5E3)
Substituting
and
, we get,
![V=\frac{4}{3} (3.14)(125)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%283.14%29%28125%29)
![V=\frac{1580}{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1580%7D%7B3%7D)
![V=523.3333 \ in^3](https://tex.z-dn.net/?f=V%3D523.3333%20%5C%20in%5E3)
Rounding off to two decimal places, we have,
![V=523.33 \ in^3](https://tex.z-dn.net/?f=V%3D523.33%20%5C%20in%5E3)
Thus, the volume of the second sphere is 523.33 in³
Part c: We need to determine the radius of the third sphere
Given that the third sphere has a diameter that is three-fourths of the diameter of the given sphere.
Hence, we have,
Diameter of the third sphere = ![\frac{3}{4} (5)=3.75](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%285%29%3D3.75)
Radius of the third sphere = ![\frac{3.75}{2} =1.875](https://tex.z-dn.net/?f=%5Cfrac%7B3.75%7D%7B2%7D%20%3D1.875)
Thus, the radius of the third sphere is 1.875 inches
Part d: We need to determine the volume of the third sphere
The formula to find the volume of the sphere is given by
![V=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%20r%5E3)
Substituting
and
, we get,
![V=\frac{4}{3} (3.14)(1.875)^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%283.14%29%281.875%29%5E3)
![V=\frac{4}{3} (3.14)(6.59)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%283.14%29%286.59%29)
![V=27.5901 \ in^3](https://tex.z-dn.net/?f=V%3D27.5901%20%5C%20in%5E3)
Rounding off to two decimal places, we have,
![V=27.59 \ in^3](https://tex.z-dn.net/?f=V%3D27.59%20%5C%20in%5E3)
Thus, the volume of the third sphere is 27.59 in³