a. The dimensions of the cube are 30 inches × 30 inches × 30 inches.
b. The volume of the cube will be 27,000 inches³
c. The volume of the sphere will be 14,130 inches³
d. The volume inside the cube that is not taken up by the sphere will be 12,870 inches³.
What is the volume of a sphere?
If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
a. The dimensions of the cube are 30 inches × 30 inches × 30 inches.
The cube has the same dimension for the length breadth and the height. Hence, the dimensions of the cube are 30 inches × 30 inches × 30 inches.
b. The volume of the cube will be 27,000 inches³
The volume of the cube is found as the power three of the side;
Volume of cube = (side)³
Volume of cube =30³
Volume of cube =27000 inches³
C. The volume of the sphere will be 14,130 inches³.
The volume of the sphere is ;
[tex]\rm V= \dfrac{4}{3} \pi r^3 \: \rm unit^3 \\\\\ V= \dfrac{4}{3} \times 3.14 (15)^3 \: \rm unit^3 \\\\ V=14130 \ inches^3[/tex]
d. The volume inside the cube that is not taken up by the sphere will be 12,870 inches³.
The volume inside the cube that is not taken up by the sphere is found by subtracting the total volume of the cube to the volume of the sphere;
ΔV=27000 – 14130
ΔV=12870 inches³
Hence, the dimensions of the cube, the volume of the cube, the volumes of the sphere and the volumes inside the cube that is not taken up by the sphere will be 30 inches × 30 inches × 30 inches, 27,000 inches, 14,130 inches³ and 12,870 inches³ respectively.
Learn more about the volume of a sphere refer:
https://brainly.com/question/381274
#SPJ2
