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

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