Area and Volume of Prisms Area and Volume of Pyramids Triangles Area and Volume of Cones Area and Volume of Cylinders 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

Area and Volumes of Prisims

Find the volume of a cube with edge 8 Category 1 10

Find the lateral area, total are and volume of a rectangular solid with length 10, width 8, and height 4.5 Category 1 20

Find the area of the figure Category 1 30

Matchsticks are rectangular prisms of wood measuring approximately: 1/10 inch by 1/10 inch by 2 inches. Matchsticks are often made from pine trees. Estimate how many matchsticks can be made from this tree (trunk diameter 2 ft.; height 80 ft.). Category 1 40

Find the weight, to the nearest kilogram, of the cement block Find the weight, to the nearest kilogram, of the cement block. Cement weighs 1700 kg/m³ Category 1 50

Area and Volume of Pyramids

Find the lateral area, total area, volume of a square pyramid with base edge 24 and slant height 13 Category 2 10

Find the volume of a regular triangular pyramid with base edge 8 and height 10. 20

A regular square pyramid has base edge 30 and total area 1920 A regular square pyramid has base edge 30 and total area 1920. What is the area of the base, the lateral area, and the slant height? Category 2 30

Find the volume of a square with a slant height 17in and surface area 800in² Category 2 40

Calculate the surface area of the given solid Calculate the surface area of the given solid. Round to the nearest tenth Category 2 50

Special Triangles

Find x and y Category 3 10

Find x Category 3 20

The altitude of an equilateral triangle is 18 inches The altitude of an equilateral triangle is 18 inches. Find the length of a side. Category 3 30

Find x and y Category 3 40

Find x and y Category 3 50

Category 4 questions follow

Two similar cones have heights 5 and 20 Two similar cones have heights 5 and 20. What is the ratio of their volumes? Category 4 10

Find the lateral area, total area, and volume of a cone with height 12 and radius 9. Category 4 20

A solid metal cylinder with radius 2 and height 2 is recast as a solid cone with radius 2. What is the height of the cone? Category 4 30

If a cone’s radius is 6 and its slant height is 1o If a cone’s radius is 6 and its slant height is 1o. What is its height, total area and volume? Category 4 40

Tim Tebow owns a ski resort in the American West Tim Tebow owns a ski resort in the American West. There’s been hardly any snow this winter, so Tim Tebow decides to order some. (a) Modeling the mountain as a cone 5,000 feet tall and 20,000 feet around the base, what is the total surface area that Tim Tebow needs to cover? (b) Suppose that Tim Tebow wants to cover the mountain with three feet of snow. What is the total volume of snow required? Category 4 50

Area and Volume of Cylinders

Find the lateral area, total area, and volume of a cylinder with radius 10in and height 7in Category 5 10

A cylinder has radius 6cm and height 4cm A cylinder has radius 6cm and height 4cm. What is the lateral area and volume? Category 5 20

A cylinder has a radius of 10 and a height of 12 A cylinder has a radius of 10 and a height of 12. Suppose that the lateral surface of the cylinder is covered with a thin coat of paint having thickness 0.1. What is the volume of the paint? (round to the nearest tenth) Category 5 30

Each tennis ball is a sphere with a radius of 3. 25 centimeters Each tennis ball is a sphere with a radius of 3.25 centimeters. Find the volume of the can of tennis balls. Round to the nearest cubic centimeter. Category 5 40

Lebron James spends the winters working at a ski lodge Lebron James spends the winters working at a ski lodge. This winter, the ski lodge has gotten a huge amount of snow, so they decide to dig a half-pipe. Assuming that they want to build a 100 meter pipe with the dimensions of the cross-section below, what is the total volume of snow that they will need to remove to create the half-pipe? Category 5 50