Page 2 6. A semicircular trough is shown. If x = 5 m and y = 1 m, how many cubic meters of fluid will this trough hold? 7. In the diagram, the base of
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1 Accerlerated Geometry Name In Class Practice: Area/Volume Per/Sec. Date (1.) Show work for credit. (2.) Leave solution in exact form unless otherwise stated. (3.) Provide the correct UNITS on all solutions. 1. The inside of a pipe 8 inches wide and inches long is coated with rust protectant. How many square inches of coating is used? 2. In the right cylinder shown, h = 1 0 and r = 3. What is the total surface area of this cylinder? 3. What is the surface area of a cube with edges of 7? 4. A hemispheric dome is needed to cover a circular region having an area of square feet. What will be the height of this dome? Answer to the nearest tenth of a foot. 5. A fermentation tank is shaped like a regular hexagonal right prism. The tank has a perimeter of 1 2 feet and a depth of 5 feet. If one cubic foot of liquid contains 7.48 gallons, about how many gallons of liquid does it take to fill this tank to its rim?
2 Page 2 6. A semicircular trough is shown. If x = 5 m and y = 1 m, how many cubic meters of fluid will this trough hold? 7. In the diagram, the base of the hemisphere (shaded area) is 250 cm 2. What is the total surface area of the hemisphere? 8. A cylindrical cake pan has a diameter of 1 0 inches and a height of 4 inches. If 220 cubic inches of cake batter is poured into the pan, how far up the sides of the pan will the batter come to the nearest tenth of an inch? 9. In the diagram, a plane is passed through a sphere at a point that is x units away from the center of the sphere. The radius of the sphere is y units. Express the cross-sectional area of intersection in terms of x and y A triangular right prism is shown. If AB = BC = 1 3, AC = 24, and CF = BE = AD = 30, what is the surface area of the prism?
3 Page A box shaped like a rectangular prism is used to hold dominoes. Each domino measures 6 cm long by 3 cm wide by 1.5 cm high. If the box measures 36cm long by 30cm wide by 1 5 cm high, how many dominoes will fit into the box? 1 2. A frustum is shown with a slant height ` of 4 in, a lower base radius r 2 of 6 in, and an upper base radius r 1 of 3 in. What is the volume of the frustum to the nearest cubic inch? p 1 3. A cube has an internal diagonal of length 4 3. What is the volume of the cube? 1 4. In the diagram, the height h of the cone is three times the radius of the cone. The volume of the cone is 343 cm 3. What is the height of the cone? 1 5. What is the volume of the largest square prism that a right cylinder with a height of 8 cm and a radius of 3 cm can contain?
4 Page The base area of a right circular cone is 25 cm 2. The height of the cone is 9 cm. What is the total surface area of the cone to the nearest square centimeter? 1 7. The radius of the sphere shown is 3 cm. What is the exact volume of the sphere? 1 8. The bases of a right prism are regular hexagons with sides of length 4. If the height of the prism is 5, what is the lateral area of the prism? 1 9. A right cylinder with a height h of 8 cm and a diameter d of 6 cm has a cone removed as shown in the diagram. Find the remaining volume. 20. In the diagram, the right cone has a height of 1 2 in. and a base circumference of 6 in. What is the lateral surface area of the cone to the nearest square inch?
5 Page A triangular pyramid has a right triangle for a base with legs of 6 and 8. The height of the pyramid is 1 2. What is the volume of the pyramid? 22. Primo Painters is hired to paint a large cylindrical water storage tank. The tank is 40 feet high with a circumference of 94 feet. It is resting on the ground, so Primo only has to paint the top and the sides of the tank. The paint Primo will be using costs $20 for each gallon can and covers 300 square feet of surface area. How much will the paint for the job cost Primo? (Remember that Primo can only buy paint in gallon containers.) 23. A right cylinder is shown. h = 1 0 and the circumference of the circular base is 8. What is the volume of the cylinder? 24. The base of a right triangular pyramid is an equilateral triangle with side lengths of 1 2 cm. The length of one of the lateral edges is 1 0 cm. What is the total surface area of this pyramid? 25. A sphere is inscribed in a cube. If the volume of the cube is cm 3, what is the volume of the sphere?
6 Page The right triangular prism shown has bases that are equilateral triangles. The height h of the prism is 4 in. and the base edges each measure 6 in. Find the exact volume of the prism. 27. Wally Wonka is trying to break a world record by making a gigantic chocolate candy. He lets chocolate slowly drip from a tank overnight and in the morning he finds that it has formed a giant cone. He measures the circumference of the cone and finds that it is 48 feet. He then measures the slant height of the cone and finds that it is 1 2 feet. To the nearest tenth, how many cubic yards of chocolate should he report is in the candy? 28. The bases of a right triangular prism have sides of 4 cm, 5 cm, and 7 cm. The volume of the prism is 1 00 cm 3. Find the height of the prism to the nearest tenth of a centimeter. 29. In the diagram, a right square pyramid is shown. The altitude h = 1 0 and the base edge e = 4. What is the volume of the pyramid? 30. In the diagram, r = 3 and x = 45. What is the volume of the remaining part of the hemisphere to the nearest tenth of a cubic unit?
7 Page A right square pyramid is shown with lateral edge k = 1 0, slant height s = 8, and base edge e = 1 2. What is the total surface area of this pyramid? 32. What is the surface area of a sphere with a radius of p 3? 3 3. A right hexagonal prism has base edges of 4 units and lateral edges of 5 units. What is its total surface area? 34. The silo shown is composed of a hemisphere and a cylinder. The total height of the silo is 50 feet and the diameter of the silo is 1 6 feet. What is the volume of the silo to the nearest cubic foot? 3 5. The right circular cylinder shown in the diagram has a height of 5 cm and a radius of 2 cm. What is the volume of this cylinder?
8 Acces format version 3.60B c EducAide Software Licensed for use by Lemont Township High School Accerlerated Geometry In Class Practice: Area/Volume 2/2/04 Answer List in units units ft gal cm in m3 y 2 x units in units cm cm cm cm units cm in units $ units ( p 3 ) cm cm p 3 in yds cm units unit units units ( p 3) units ft cm 3 Catalog List 1. GEO KG GEO KG 2 3. GEO KE 3 4. GEO KK GEO KD GEO KF 7 7. GEO KK GEO KF GEO KK GEO KE GEO KD GEO KH GEO KD GEO KH GEO KF GEO KI GEO KJ GEO KE GEO KM GEO KI GEO KH GEO KG GEO KF GEO KI GEO KM GEO KD GEO KH GEO KD GEO KH GEO KJ GEO KI GEO KK GEO KE GEO KJ GEO KF 2
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