6. 7. Allan keeps tropical fish. His aquarium is 4 feet long, 1 foot wide, and 2 feet tall. Each fish needs at least 0.5 ft3 of water. What is the maximum number of fish that he can keep in the aquarium? Cindy has a chocolate box whose length is 12 cm, height of 8 cm, and width of 6 cm. Find the volume of the box? 8. A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank? 9. A chocolate milk container in the form of a rectangular prism is 5 cm long, 3 cm wide, and 9 cm high. How many cubic centimeters of chocolate milk can it hold? 10. Find the volume of a right circular cone-shaped building with a height of 9 cm and a radius base of 7 cm.
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Answer:
7. The volume of the aquarium is 4 ft x 1 ft x 2 ft = 8 cubic feet. Dividing the volume of the aquarium by the volume of water needed for one fish gives us 8 ft3 ÷ 0.5 ft3/fish = 16 fish. Therefore, Allan can keep a maximum of 16 fish in the aquarium.
8. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. Rearranging the formula, we get h = V/πr^2. Substituting the given values, we have h = 44 m^3/(π x 3.5 m)^2 = 1.5 m. Therefore, the tank is 1.5 meters high.
9. The volume of the rectangular prism is the product of its length, width, and height. Therefore, the volume is 5 cm x 3 cm x 9 cm = 135 cubic centimeters.
10. The formula for the volume of a right circular cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we have V = (1/3)π(7 cm)^2(9 cm) = 220.44 cubic centimeters. Therefore, the volume of the cone-shaped building is approximately 220.44 cubic centimeters.