Rectangular Prism SA

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Rectangular Prism SA · Grade 6 · Worksheet 2

1. Mere is constructing a rectangular prism-shaped display case with length 32 cm, width 24 cm, and height 20 cm. What is the total surface area of the display case in square centimeters? Answer: 3776 Solution: Identify the dimensions: length (l) = 32 cm, width (w) = 24 cm, height (h) = 20 cm. Use the formula SA = 2lw + 2lh + 2wh. Calculate 2lw = 2 × 32 × 24 = 2 × 768 = 1536.
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 32 cm, width (w) = 24 cm, height (h) = 20 cm. Step 2: Use the formula SA = 2lw + 2lh + 2wh. Step 3: Calculate 2lw = 2 × 32 × 24 = 2 × 768 = 1536. Step 4: Calculate 2lh = 2 × 32 × 20 = 2 × 640 = 1280. Step 5: Calculate 2wh = 2 × 24 × 20 = 2 × 480 = 960. Step 6: Add the three results: 1536 + 1280 + 960 = 3776. The answer is 3776 square centimeters.

2. Tane is building a rectangular prism-shaped planter box for his garden. The planter box has a length of 160 cm, a width of 90 cm, and a height of 45 cm. He wants to line the inside of the box with a waterproof liner. However, the liner will only cover the bottom and the four side walls (not the top opening). What is the total area of the waterproof liner Tane needs, in square centimeters? Answer: 36900 Solution: Identify the dimensions: length = 160 cm, width = 90 cm, height = 45 cm. Calculate the area of the bottom face (length × width): 160 × 90 = 14,400 square cm.
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 160 cm, width = 90 cm, height = 45 cm. Step 2: Calculate the area of the bottom face (length × width): 160 × 90 = 14,400 square cm. Step 3: Calculate the area of the two longer side walls (length × height): Each longer side wall: 160 × 45 = 7,200 square cm. Two longer side walls: 7,200 × 2 = 14,400 square cm. Step 4: Calculate the area of the two shorter side walls (width × height): Each shorter side wall: 90 × 45 = 4,050 square cm. Two shorter side walls: 4,050 × 2 = 8,100 square cm. Step 5: Add all the areas together: 14,400 (bottom) + 14,400 (longer sides) + 8,100 (shorter sides) = 36,900 square cm. The total area of the waterproof liner Tane needs is 36,900 square centimeters.

3. Mason is painting a large wooden storage chest shaped like a rectangular prism. The chest has a length of 12 inches, a width of 10 inches, and a height of 15 inches. He needs to paint all six faces, including the bottom. One can of paint covers 100 square inches. How many cans of paint does Mason need to buy to completely paint the chest? Answer: 9 Solution: Identify the dimensions: length = 12 in, width = 10 in, height = 15 in. Calculate the area of the top and bottom faces: lw = 12 × 10 = 120 sq in. Two faces: 2 × 120 = 240 sq in.
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 12 in, width = 10 in, height = 15 in. Step 2: Calculate the area of the top and bottom faces: lw = 12 × 10 = 120 sq in. Two faces: 2 × 120 = 240 sq in. Step 3: Calculate the area of the front and back faces: lh = 12 × 15 = 180 sq in. Two faces: 2 × 180 = 360 sq in. Step 4: Calculate the area of the left and right faces: wh = 10 × 15 = 150 sq in. Two faces: 2 × 150 = 300 sq in. Step 5: Total surface area: 240 + 360 + 300 = 900 sq in. Step 6: Each can covers 100 sq in. Number of cans = 900 ÷ 100 = 9. Step 7: Since 9 is a whole number, no rounding up is needed. The answer is 9 cans.