Question

Question 1- The Rockefeller Center Christmas Tree has a volume of 88,548 ft3. It has a height of 94 ft. Find the radius.

Question 2-Janet made a model of the Great Pyramid of Giza in Egypt. The length of the base of her pyramid is 9 inches and the width is 5 inches. The height of her pyramid is 12 inches. Find the volume of her pyramid.

Question 3- Jaquan is a basketball star. The basketball has a radius of 5 inches. What is the volume of the basketball?

Answer 1

Question 1:
`r=29.99\ ft`

Question 2:
`V=180\ in^3`

Question 3:
`V=523.59\ in^3`

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:

`V=(1)/(3)\pi r^2h`

Where "r" is the radius and "h" is the height.

In this case we know that:

`V=88,548 ft^3\\h= 94\ ft`

Then, substituting values into the formula and solving for "r", we get:

`88,548=(1)/(3)\pi r^2(94)\\\\(3(88,548))/(94\pi)=r^2\\\\\sqrt{(3(88,548))/(94\pi)}=r\\\\r=29.99\ ft`

2- We can use this formula for calculate the volume of the rectangular pyramid:

`V=(1)/(3) lwh`

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:

`l= 9\ in\\w=5\ in\\h=12\ in`

We can substitute values into the formula to find the volume of her pyramid:

`V=(1)/(3) (9\ in)(5\ in)(12\ in)=180\ in^3`

3- The formula for calculate the volume of a sphere is:

`V=(4)/(3)\pi r^3`

Where "r" is the radius.

Knowing that the the radius of the basketball is:

`r=5\ in`

We get that its volume is:

`V=(4)/(3)\pi (5\ in)^3=523.59\ in^3`