Rectangular Prism SA

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Rectangular Prism SA · Grade 6 · Worksheet 3

1. 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.

2. Mere is painting a rectangular prism-shaped planter box. The box has a length of 18 cm, a width of 12 cm, and a height of 14 cm. What is the total surface area she needs to paint? Answer: 1272 Solution: Identify the dimensions: length (l) = 18 cm, width (w) = 12 cm, height (h) = 14 cm. Calculate the area of the top and bottom faces: 2 × l × w = 2 × 18 × 12 = 2 × 216 = 432.
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 18 cm, width (w) = 12 cm, height (h) = 14 cm. Step 2: Calculate the area of the top and bottom faces: 2 × l × w = 2 × 18 × 12 = 2 × 216 = 432. Step 3: Calculate the area of the front and back faces: 2 × l × h = 2 × 18 × 14 = 2 × 252 = 504. Step 4: Calculate the area of the left and right faces: 2 × w × h = 2 × 12 × 14 = 2 × 168 = 336. Step 5: Add all the areas together: 432 + 504 + 336 = 1272. The total surface area is 1272 square centimeters.

3. 2³ × (15 - 7) + 24 ÷ 3 = ? Answer: 72 Solution: Handle the exponent first. 2³ means 2 × 2 × 2 = 8. 8 × (15 - 7) + 24 ÷ 3 Evaluate inside the parentheses.
   Full step-by-step solution

   Let's solve step by step using the order of operations (PEMDAS/BODMAS). Step 1: Handle the exponent first. 2³ means 2 × 2 × 2 = 8. So the expression becomes: 8 × (15 - 7) + 24 ÷ 3 Step 2: Evaluate inside the parentheses. 15 - 7 = 8 Now we have: 8 × 8 + 24 ÷ 3 Step 3: Perform multiplication and division from left to right. First, 8 × 8 = 64 Then, 24 ÷ 3 = 8 Now we have: 64 + 8 Step 4: Perform addition. 64 + 8 = 72 Final answer: 72

4. A rectangular prism-shaped swimming pool has dimensions: length = 15.2 meters, width = 8.5 meters, and depth = 2.3 meters. The pool has a tiled border around the top edge that covers 0.4 meters down from the top on all four side walls. What is the total surface area of the tiled border in square meters? Answer: 18.96 Solution: Identify the tiled surfaces. The border covers 0.4 meters down from the top on all four side walls (front, back, left, right).
   Full step-by-step solution

   Step 1: Identify the tiled surfaces. The border covers 0.4 meters down from the top on all four side walls (front, back, left, right). Step 2: Calculate the area of the front wall border: length × border height = 15.2 × 0.4 = 6.08 square meters Step 3: Calculate the area of the back wall border: same as front = 15.2 × 0.4 = 6.08 square meters Step 4: Calculate the area of the left wall border: width × border height = 8.5 × 0.4 = 3.4 square meters Step 5: Calculate the area of the right wall border: same as left = 8.5 × 0.4 = 3.4 square meters Step 6: Add all four border areas: 6.08 + 6.08 + 3.4 + 3.4 = 18.96 square meters Step 7: The total surface area of the tiled border is 18.96 square meters.

5. Liam is wrapping a birthday present for his friend. The box is a rectangular prism that measures 24 cm long, 18 cm wide, and 12 cm high. He needs to calculate the total surface area to know how much wrapping paper to buy. What is the total surface area of the box in square centimeters? Answer: 1872 Solution: A rectangular prism has 6 faces. Each pair of opposite faces are equal rectangles. Surface Area = 2 * (length * width + length * height + width * height) Identify the given dimensions.
   Full step-by-step solution

   Let's find the total surface area of the rectangular prism box. Step 1: Understand the formula for the surface area of a rectangular prism. A rectangular prism has 6 faces. Each pair of opposite faces are equal rectangles. The formula is: Surface Area = 2 * (length * width + length * height + width * height) Step 2: Identify the given dimensions. Length (l) = 24 cm Width (w) = 18 cm Height (h) = 12 cm Step 3: Calculate the area of the three different types of rectangular faces. Area of the front/back faces (length * height) = 24 * 12 = 288 Area of the left/right faces (width * height) = 18 * 12 = 216 Area of the top/bottom faces (length * width) = 24 * 18 = 432 Step 4: Add these three areas together. 288 + 216 + 432 = 936 Step 5: Multiply by 2 because there are two of each type of face. Total Surface Area = 2 * 936 = 1872 Step 6: State the final answer with units. The total surface area of the box is 1872 square centimeters. ANSWER: 1872