Surface area and Volume: Cylinders, Prisms, Cones, Pyramids, Spheres Name:___________________________ Per:___ Show all of your work, including labeled diagrams, and units! 1. Construct the cone and the pyramid attached to this worksheet. a. Find the volume and surface area of the pyramid. Show your work. b. Find the volume and surface area of the cone. Show your work. 2. Find the total surface area and volume of the rectangular pyramid at right. Volume =__________________ Surface Area = _______________ 3. Find the volume and surface area of the sphere. Volume =__________________ Surface Area = _______________ 4. We aren’t able to directly measure the radius or diameter of the Earth, but we can measure the circumference. The circumference is approximately 25,000 miles. If we know that about 71% of the Earth’s surface is covered by oceans, find the surface area of the oceans on Earth (in square miles). 5. Rebecca bought a colossal ice cream cone like the one shown. If the top is a hemisphere and the ice cream completely fills the cone, how much ice cream did Rebecca receive? 6. Find the volume and surface area of a pyramid if it has a regular triangular base with a perimeter of 36cm, and the pyramid’s height of 15cm. Try to sketch the pyramid with dimensions before finding volume and surface area. 7. While making his lunch, Alexander sliced off a portion of his grapefruit. If the area of the cross-‐section of the slice (shaded at right) was 3 inches squared, and if the diameter of the grapefruit was 5 inches, find the distance between the center of the grapefruit and the slice. Assume the grapefruit is a sphere. 8. The solid at right is an example of a truncated pyramid. It is formed by slicing and removing the top of the pyramid so that the slice is parallel to the base of the pyramid. If the original height of the square based pyramid was 12 cm, find the volume of this truncated pyramid.
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