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.
ScanSolve AI Answer
Here's how to solve the problem: The solid is a right triangular prism. From the diagram: • The base is a right-angled triangle with legs 7 cm and 24 cm. • The height of the prism is 40 cm. Step 1: Calculate |NC|. |NC| is the hypotenuse of the right-angled triangular base. Using the Pythagorean theorem: |NC|^2 = 7^2 + 24^2 |NC|^2 = 49 + 576 |NC|^2 = 625 |NC| = sqrt(625) |NC| = 25 cm The length of |NC| is 25 cm. Step 2: Calculate the area of the triangular base. The area of a right-angled triangle is (1)/(2) × base × height. Area of base = (1)/(2) × 7 cm × 24 cm Area of base = (1)/(2) × 168 cm^2 Area of base = 84 cm^2 Step 3: Calculate the volume of the solid. The volume of a prism is given by the formula: Volume = Area of base × Height of prism. Volume = 84 cm^2 × 40 cm Volume = 3360 cm^3 The volume of the solid is 3360 cm^3. Step 4: Calculate the perimeter of the triangular base. The perimeter of the base is the sum of its three sides. Perimeter of base = 7 cm + 24 cm + 25 cm Perimeter of base = 56 cm Step 5: Calculate the total surface area of the solid. The total surface area of a prism is given by the formula: Total Surface Area = 2 × Area of base + Perimeter of base × Height of prism. Total Surface Area = 2 × 84 cm^2 + 56 cm × 40 cm Total Surface Area = 168 cm^2 + 2240 cm^2 Total Surface Area = 2408 cm^2 The total surface area of the solid is 2408 cm^2. 3 done, 2 left today. You're making progress.