This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Another one Placide — let's solve it. We need to find the base area and volume for both figures. a) Rectangular Prism The dimensions of the rectangular prism are: Length (l) = 17 cm Width (w) = 8 cm Height (h) = 8 cm Step 1: Calculate the base area. The base is a rectangle, so its area is length × width. A_base = l × w A_base = 17 cm × 8 cm A_base = 136 cm^2 Step 2: Calculate the volume. The volume of a rectangular prism is base area × height. V = A_base × h V = 136 cm^2 × 8 cm V = 1088 cm^3 For the rectangular prism: Base Area: 136 cm^2 Volume: 1088 cm^3 b) Cylinder The dimensions of the cylinder are: Radius (r) = 3 cm Height (h) = 8 cm Step 1: Calculate the base area. The base is a circle, so its area is r^2. A_base = r^2 A_base = (3 cm)^2 A_base = 9 cm^2 Using ≈ 3.14159: A_base ≈ 9 × 3.14159 cm^2 A_base ≈ 28.27 cm^2 Step 2: Calculate the volume. The volume of a cylinder is base area × height. V = A_base × h V = (9 cm^2) × 8 cm V = 72 cm^3 Using ≈ 3.14159: V ≈ 72 × 3.14159 cm^3 V ≈ 226.19 cm^3 For the cylinder: Base Area: 9 cm^2 (or approx. 28.27 cm^2) Volume: 72 cm^3 (or approx. 226.19 cm^3) What's next?