A globe has a diameter of 12 inches. It fits inside a cube-shaped box that has a side length of 12 inches. What is
the volume, rounded to the nearest hundredth of a cubic inch, of the space inside the box that is not taken up by the globe?
the volume, rounded to the nearest hundredth of a cubic inch, of the space inside the box that is not taken up by the globe?
The volume of a globe (sphere) is:
4
--- πr³ {volume of a sphere}
3
The radius of the globe is 6. {radius is half the diameter}
Volume of the globe
V = (4/3)(3.14)(6³) {substituted 6 for r and 3.14 for π into volume formula}
≈ (4/3)(3.14)(216) {evaluated exponent}
≈ 904.32 in³ {multiplied}
The volume of a cube-shaped box:
V = s³ {one side, cubed}
Volume of the box
V = 12³ {substituted 12, in for s, into volume formula}
= 1728 in³ {evaluated exponent}
The space inside the box not taken up by the globe
≈ 1728 - 904.32 {volume of box minus volume of globe}
≈ 823.68 in³ {subtracted}
Ask Algebra House
4
--- πr³ {volume of a sphere}
3
The radius of the globe is 6. {radius is half the diameter}
Volume of the globe
V = (4/3)(3.14)(6³) {substituted 6 for r and 3.14 for π into volume formula}
≈ (4/3)(3.14)(216) {evaluated exponent}
≈ 904.32 in³ {multiplied}
The volume of a cube-shaped box:
V = s³ {one side, cubed}
Volume of the box
V = 12³ {substituted 12, in for s, into volume formula}
= 1728 in³ {evaluated exponent}
The space inside the box not taken up by the globe
≈ 1728 - 904.32 {volume of box minus volume of globe}
≈ 823.68 in³ {subtracted}
Ask Algebra House
