Exercises

Round all answers to 1 decimal place.

1. Kalam has a mold for making spherical popsicles, each with a diameter of \(4.5\) cm. She has \(1\) L of fruit juice. Does Kalam have enough juice to make \(24\) popsicles?
2. Snow cones are served at a summer carnival in conical cups with a radius of \(5\) cm and a height of \(10\) cm. The cup is filled with snow cone slush then an extra hemisphere of slush is piled on top. If the hemisphere and the cup have the same radius, calculate the volume of slush in one snow cone.
3. The Dominion Astrophysical Observatory in Victoria, British Columbia, is a cylindrical shape with a dome shaped roof. The diameter of the cylinder is \(20.2\) m and the height is \(22.3\) m. The outside of the structure needs to be repainted. What is the surface area that needs to be painted, including the roof?

   

4. A hemisphere is half of a sphere.
   1. Calculate the surface area of a hemisphere with diameter \(11\) cm.
   2. Show how to develop a general formula for the surface area of a hemisphere in terms of its radius.

   

5. Jamal is making an aromatic ornament by pushing cloves into the peel of a spherical orange with a diameter of \(8\) cm. The part of each clove that will be visible on the surface of the orange is approximately a square with side lengths of \(5\) mm.

   How many cloves will Jamal need if he wants to completely cover the surface of the orange?

   

6. A manufacturer is deciding whether to use a rectangular prism or a cylinder to package three tennis balls with a radius of \(3.3\) cm. Which package would have less empty space?
7. 1. A sphere and a cone have the same volume and radius. What is the height of the cone \(h\) in terms of the radius \(r\)?
   2. A large spherical balloon has three times the volume of a smaller spherical balloon. What is the radius of the large balloon \(R\) in terms of the radius of the small balloon \(r\)?

8. Liam is creating a three dimensional model of a head. He uses a \(7.4\) L styrofoam ball and removes one-sixth of the ball by cutting a wedge whose tip is a diameter of the sphere. What is the surface area that needs to be painted on his model? Include the inside of the “mouth”.

   

9. The Earth is made up of an inner core, outer core, mantle, and crust. The crust makes up about \(1\%\) of the Earth’s volume. The radius of the Earth is \(6371\) km. What is the depth of the Earth's crust?

   

   Source: Earth's Layers - bubaone/iStock/Getty Images

10. Planet Aqua is completely covered by an ocean of a consistent depth. The radius to the ocean floor of the planet is \(2000\) km. The volume of the water in the ocean is equal to the volume of material in the planet itself. Calculate the depth of the ocean.