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 are the solutions to the problems: a) Step 1: Identify the relationship between radius, height, and slant height. The radius (r), height (h), and slant height (l) of a cone form a right-angled triangle. We can use the Pythagorean theorem: r^2 + h^2 = l^2 Step 2: Substitute the given values and solve for h. Given r = 4.2 cm and l = 11 cm. (4.2)^2 + h^2 = (11)^2 17.64 + h^2 = 121 h^2 = 121 - 17.64 h^2 = 103.36 h = sqrt(103.36) h ≈ 10.1666 cm Step 3: Round the height to 3 significant figures. h ≈ 10.2 cm Thus, the height of the cone is 10.2 cm (correct to 3 significant figures). b) Step 1: State the formula for the volume of a cone. The volume (V) of a cone is given by: V = (1)/(3) r^2 h Step 2: Substitute the values and calculate the volume. Using r = 4.2 cm and the more precise value of h = sqrt(103.36) cm from part (a): V = (1)/(3) × × (4.2)^2 × sqrt(103.36) V = (1)/(3) × × 17.64 × sqrt(103.36) V ≈ (1)/(3) × 3.14159265 × 17.64 × 10.166612 V ≈ 186.662 cm^3 Step 3: Round the volume to an appropriate number of significant figures (e.g., 3 significant figures). V ≈ 187 cm^3 The volume of the cone is 187 cm^3. What's next? Send 'em!