Question

question 1
a cube has an edge - length of 68 inches. a solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. to the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?
a) 149,790
b) 104,500
c) 100,955
d) 310,800

Explanation:

Step1: Calculate cube volume

The volume formula for a cube is $V_{cube}=s^3$, where $s = 68$ inches. So $V_{cube}=68^3=68\times68\times68 = 314432$ cubic - inches.

Step2: Calculate sphere volume

The volume formula for a sphere is $V_{sphere}=\frac{4}{3}\pi r^3$, with $r = 34$ inches. So $V_{sphere}=\frac{4}{3}\pi\times34^3=\frac{4}{3}\pi\times39304\approx\frac{4}{3}\times3.14\times39304\approx164636.21$ cubic - inches.

Step3: Calculate the remaining volume

The volume of the space not taken up by the sphere in the cube is $V = V_{cube}-V_{sphere}$. So $V=314432 - 164636.21\approx149796\approx149790$ (to the nearest cubic inch).

Answer:

A. 149,790