MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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]