Solve the following completely. Show complete and neat solutions. This will be collected first period tomorrow morning. Be ready to explain your solutions in class.
1. Angge the ant walks through all vertices once along the edges of a cube using the shortest possible route. If the total distance she covered is 49 cm., what is the surface area and volume of the cube?
2. A tennis ball fits exactly inside a cube of side length 6 cm. What is the volume of the sphere?
3. A cone of height 7 cm. has a radius of 1.5 cm. If a semi-spherical ice cream scoop is placed on top of it, what is the total volume formed by the ice cream cone?
4. A uniform hexagonal prism has a side length of 8 cm. What is its volume?
5. If a rectangular prism block of wood has dimension 5 cm x 4 cm x 6 cm and cost $60 , what is the fair price in dollars of a 15 cm x 24 cm x 48 cm block of the same type if price is determined solely by volume?
6. What percent of the volume of a 10 '' x 10'' x 10'' box can be filled with 4'' x 4'' x 4'' wooden cubes? Express your answer as a decimal to the nearest tenth.
7. A hollow piece of cylindrical pipe has an outside radius of 2 inches and an inside radius of 1.9 inches. The pipe is 3 feet long. What is the surface area and volume of the pipe? Use Pi=3.14.
8. The slant height of a cone is 51 cm , and the height from the vertex to the center of the base is 45 cm . What is the number of cubic centimeters in the volume of the cone? The answer is x Pi . What is x?
9. A wooden model of a square pyramid has a base edge of 42 cm and an altitude of 21 cm. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and frustum. The height of the smaller pyramid is 9 cm. What is the volume of the frustrum?
10. A 15 cm x 11 cm x 7 cm box is to be filled with 3 cm x 3 cm x 3 cm cubes. The extra spaces would then be filled with 1 cm x 1 cm 1 cm cubes. If the box is to be filled with as many 3 cm cubes as possible before being filled by 1 cm cubes, and that there would be no extra space after, how many cubes will be needed in all?
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