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.

Answer 1

Answer:

Question 1: $r=29.99\ ft$

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

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

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:

$V=\frac{1}{3}\pi r^2h$

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:

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

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

$V=\frac{1}{3} lwh$

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:

$V=\frac{1}{3} (9\ in)(5\ in)(12\ in)=180\ in^3$

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

$V=\frac{4}{3}\pi r^3$

Where "r" is the radius.

Knowing that the the radius of the basketball is:

$r=5\ in$

We get that its volume is:

$V=\frac{4}{3}\pi (5\ in)^3=523.59\ in^3$