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- Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?If the tank in Exercises 41 needs to be painted and 1 pint of paint covers 50ft2, how many pints are needed to paint the exterior of the storage tank? A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gallon of gasoline, what is the total storage capacity of the tank measured in gallons?
- The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the length of each edge of the original cube?The roof of the house shown needs to be reshingled. a Considering that the front and back sections of the roof have equal areas, find the total area to be reshingled. b If roofing is sold in squares each covering 100ft2, how many squares are needed to complete the work? c To remove old shingles and replace with new shingles costs 97.50 per square. What is the cost of reroofing?
- If the radius length of one sphere is three times as long as the radius length of another sphere, how do the surface areas of the spheres compare? How do the volume compare?Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat mixture used to fill the raised bed costs 15.75 per cubic yard. What is the total cost of the ingredients used to fill the raised garden?A steel forging in the shape of a right circular cone weighs 214.6 pounds. The base of the cone has a diameter of 8.72 inches. If the steel in the forging weighs 490.5 pounds per cubic foot, what is the height of the cone? Round the answer to the nearest tenth inch.