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Mathematics, 26.02.2021 21:30 iicekingmann

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1. The body of a rocket ship can be modeled as a large cylinder with a cone on the very top. The height of the cylinder is 88 m, and the height of the cone is 11 m. The radius of each is the same - 2.5 m. Calculate the volume of the rocket ship to the nearest m​ 3​ .

2. A trash can is filled with golf balls. Assume that the trash can is a perfect cylinder and that each golf ball is a perfect sphere. The radius and height of the trash can are 18 inches and 36 inches, respectively. The radius of each golf ball is 1.68 inches. There are 1,292 golf balls in the trash can. Calculate the volume of empty space in the trash can.

3. SpongeBob’s body (including his square pants) can be modeled as a rectangular prism, and his arms and legs can be modeled as narrow cylinders. The base of the prism is 2 inches by 2 inches, and its height is 3 inches. Each of the four cylinders has a height of 1 inch and a radius of 0.1 inches. Since his body is a sponge, there are also empty spheres within it. If there are 15 empty spheres in his body, each with a radius of 0.3 inches, what is the total “solid” volume of SpongeBob? Round to the nearest hundredth of an inch.

4. A scale model of the Great Pyramid of Khufu has a volume of 21.88 m​ 3​ . If the scale factor for the two pyramids is 49, what is the volume of the actual Great Pyramid of Khufu? Round to the nearest m​ 3​ .

5.The largest ice cream cone ever created held 1,080 liters (1,080,000 cm​ 3​ ) of ice cream. A typical sugar cone has a height of only 11.75 cm. If the ratio of volumes between the world record cone and a typical sugar cone is 18,011:1, what was the height in meters of the world record ice cream cone? Round to the nearest meter. There is 100 cm in 1 m.

6. The most widely accepted theory of how our moon formed is called the giant impact theory. According to this theory, two planets crashed into each other, combining to form a single planet (the Earth), while some of the debris collected in an orbit around the Earth to form the moon. The two planets that collided are often referred to as Proto-Earth and Theia. The radius of the Earth is 3,958.8 miles, and the radius of the moon is 1,079.4 miles. Calculate the radius of Proto Earth to the nearest tenth of a mile. Assume that all four celestial bodies are perfect spheres, that Proto-Earth and Theia have identical volumes, and that no other mass was lost in the collision.

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