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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Q9. Find the Volume of the triangular prism a) The volume of a prism is given by the formula V = A_base × L, where A_base is the area of the base and L is the length (or height) of the prism. For a triangular prism, the base is a triangle, and its area is A_triangle = (1)/(2) × base × height. Given: Base of the triangle (b) = 12 cm Height of the triangle (h_t) = 10 cm Length of the prism (L) = 20 cm Step 1: Calculate the area of the triangular base. A_base = (1)/(2) × b × h_t A_base = (1)/(2) × 12 cm × 10 cm A_base = 60 cm^2 Step 2: Calculate the volume of the triangular prism. V = A_base × L V = 60 cm^2 × 20 cm V = 1200 cm^3 Answer: 1200 cm^3 b) For question 9b, the problem asks for the volume of a triangular prism, but the accompanying diagram shows a rectangular prism. I will solve for a triangular prism, assuming the base of the triangle is 8 inches, the height of the triangle is 8 inches (derived from the square base shown in the diagram), and the length of the prism is 12 inches. Given (based on assumption for triangular prism): Base of the triangle (b) = 8 in Height of the triangle (h_t) = 8 in Length of the prism (L) = 12 in Step 1: Calculate the area of the triangular base. A_base = (1)/(2) × b × h_t A_base = (1)/(2) × 8 in × 8 in A_base = 32 in^2 Step 2: Calculate the volume of the triangular prism. V = A_base × L V = 32 in^2 × 12 in V = 384 in^3 Answer: 384 in^3 Q10. What is the Volume of a cone with a radius of 5 cm and a height of 8 cm? The volume of a cone is given by the formula V = (1)/(3) r^2 h. Given: Radius (r) = 5 cm Height (h) = 8 cm Step 1: Substitute the given values into the formula. V = (1)/(3) (5 cm)^2 (8 cm) Step 2: Calculate the square of the radius. V = (1)/(3) (25 cm^2) (8 cm) Step 3: Multiply the numerical values. V = (200)/(3) cm^3 Answer: (200)/(3) cm^3 Send me the next one 📸