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- Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?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 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?
- Examine several rectangles, each with an area of 36 in2, and find the dimensions of the rectangle that has the smallest perimeter. What type of figure has the smallest perimeter?Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.When the rectangle in the accompanying drawing whose dimensions are 16 by 9 is cut into pieces and rearranged, a square can be formed. What is the perimeter of this square?
- 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?The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.