Answer:
Question 1: [tex]r=29.99\ ft[/tex]
Question 2: [tex]V=180\ in^3[/tex]
Question 3: [tex]V=523.59\ in^3[/tex]
Step-by-step explanation:
1- Let's assume that the Rockefeller Center Christmas Tree is a cone.
This formula is used to find the volume of a cone:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and  "h" is the height.
In this case we know that:
[tex]V=88,548 ft^3\\h= 94\ ft[/tex]
Then, substituting values into the formula and solving for "r", we get:
[tex]88,548=\frac{1}{3}\pi r^2(94)\\\\\frac{3(88,548)}{94\pi}=r^2\\\\\sqrt{\frac{3(88,548)}{94\pi}}=r\\\\r=29.99\ ft[/tex]
2- We can use this formula for calculate the volume of the rectangular pyramid:
[tex]V=\frac{1}{3} lwh[/tex]
Where "l" is the length of the base, "w" is the width of the base and "h" is the height of the pyramid.
Knowing that:
[tex]l= 9\ in\\w=5\ in\\h=12\ in[/tex]
We can substitute values into the formula to find the volume of her pyramid:
[tex]V=\frac{1}{3} (9\ in)(5\ in)(12\ in)=180\ in^3[/tex]
3- The formula for calculate the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where "r" is the radius.
Knowing that the the radius of the basketball is:
[tex]r=5\ in[/tex]
We get that its volume is:
[tex]V=\frac{4}{3}\pi (5\ in)^3=523.59\ in^3[/tex]
