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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Here are the volumes of the given shapes: a) This is a rectangular prism. Step 1: Identify the dimensions. The length l = 8 cm, width w = 5 cm, and height h = 3 cm. Step 2: Apply the formula for the volume of a rectangular prism. The volume V = l × w × h. V_a = 8 cm × 5 cm × 3 cm Step 3: Calculate the volume. V_a = 40 cm^2 × 3 cm V_a = 120 cm^3 b) This is a cylinder. Step 1: Identify the dimensions. The diameter d = 14 cm, so the radius r = (14)/(2) = 7 cm. The height h = 5 cm. Step 2: Apply the formula for the volume of a cylinder. The volume V = r^2 h. V_b = × (7 cm)^2 × 5 cm Step 3: Calculate the volume. V_b = × 49 cm^2 × 5 cm V_b = 245 cm^3 Using ≈ 3.14159: V_b ≈ 245 × 3.14159 cm^3 V_b ≈ 769.69 cm^3 c) This is a triangular prism. Step 1: Identify the dimensions of the triangular base and the prism's length. The base of the triangle b_t = 8 cm, the height of the triangle h_t = 6 cm. The length of the prism L = 20 cm. Step 2: Calculate the area of the triangular base. The area of the base A = (1)/(2) × b_t × h_t. A_c = (1)/(2) × 8 cm × 6 cm A_c = 24 cm^2 Step 3: Apply the formula for the volume of a prism. The volume V = A × L. V_c = 24 cm^2 × 20 cm Step 4: Calculate the volume. V_c = 480 cm^3 d) This is a square pyramid. Step 1: Identify the dimensions of the square base and the pyramid's height. The side length of the square base s = 6 cm. The height of the pyramid h_p = 4 cm. Step 2: Calculate the area of the square base. The area of the base A = s^2. A_d = (6 cm)^2 A_d = 36 cm^2 Step 3: Apply the formula for the volume of a pyramid. The volume V = (1)/(3) × A × h_p. V_d = (1)/(3) × 36 cm^2 × 4 cm Step 4: Calculate the volume. V_d = 12 cm^2 × 4 cm V_d = 48 cm^3 Send me the next one 📸