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
You're on a roll — Step 1: Find the volume of the pyramid. The formula for the volume of a pyramid is given as V = (1)/(3)Ah, where A is the area of the base and h is the height. From the image: • The base is a regular pentagon with a side length (s) of 6 cm. • The height (h) of the pyramid is 10 cm. First, calculate the area of the regular pentagonal base (A). The formula for the area of a regular pentagon with side length s is: A = (5s^2)/(4(180^)5) = (5s^2)/(4(36^)) Substitute s = 6 cm: A = 5 × (6 cm)^24(36^) A = 5 × 36 cm^24(36^) A = 180 cm^24(36^) A = (45)/((36^)) cm^2 Using (36^) ≈ 0.72654: A ≈ (45)/(0.72654) cm^2 ≈ 61.937 cm^2 Now, calculate the volume (V) of the pyramid: V = (1)/(3)Ah Substitute the calculated area and the given height: V = (1)/(3) × ((45)/((36^))) cm^2 × 10 cm V = (150)/((36^)) cm^3 Using the approximate value for (36^): V ≈ (150)/(0.72654) cm^3 V ≈ 206.457 cm^3 Rounding to two decimal places: 206.46 cm^3 Step 2: Find the volume of the sphere. The formula for the volume of a sphere is given as V = (4)/(3) r^3. From the image: • The radius (r) is 60 mm. • Use = 3.14. • The answer should be given to the nearest cubic centimetre. First, convert the radius from millimeters to centimeters: r = 60 mm = 6 cm Now, substitute the values into the volume formula: V = (4)/(3) × 3.14 × (6 cm)^3 V = (4)/(3) × 3.14 × (6 × 6 × 6) cm^3 V = (4)/(3) × 3.14 × 216 cm^3 V = 4 × 3.14 × (216)/(3) cm^3 V = 4 × 3.14 × 72 cm^3 V = 12.56 × 72 cm^3 V = 904.32 cm^3 Rounding to the nearest cubic centimetre: 904 cm^3 Send me the next one 📸