Question

An interior designer is buying fabric to cover throw pillows for a master bedroom. She needs material to cover 6 pillows—3 rectangle-shaped, 2 cylinder-shaped, and one sphere-shaped. The rectangles are 18 inches by 12 inches by 2 inches. The cylinders are 12 inches high and have a radius of 7 inches. The sphere has a radius of 10 inches. a. What is the surface area of each rectangle-shaped pillow?
b. What is the surface area of each cylinder-shaped pillow?
c. What is the surface area of the sphere-shaped pillow?
d. What is the total surface area for all 6 pillows?
the designer also needs to buy stuffing for the pillows.
  e. What is the volume of each rectangle-shaped pillow?
f. What is the volume of each cylinder-shaped pillow?
g. What is the volume of the sphere-shaped pillow?
h. What is the total volume needed to stuff all the pillows

Answer 1

Answer:

• a. 552 square inches
• b. 835.7 square inches
• c. 1256.6 square inches
• d. 4584 square inches
• e. 432 cubic inches
• f. 1847.3 cubic inches
• g. 4188.8 cubic inches
• h. 9179.3 cubic inches

Step-by-step explanation:

a-c. The area formulas for these figures are ...

  rectangular prism: A = 2(lw +h(l+w))

  cylinder: A = 2πr(r +h)

  sphere: A = 4πr^2

d. The total will be the sum of products: area of each pillow times the number of that type

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e-g. The volume formulas for these figures are ...

  rectangular prism: V = lwh

  cylinder: V = πr^2h

  sphere: V = (4π/3)r^3

h. As with area, the total volume is the sum of products: volume of each pillow times the number of that type.