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 for problems 1, 2, and 3: 1. What is the perimeter of the pentagon below? Step 1: Identify the shape and its properties. The shape is a regular pentagon, which has 5 equal sides. The length of one side is given as 3.2 cm. Step 2: Use the formula for the perimeter of a regular pentagon. The perimeter P is the sum of the lengths of all sides. P = number of sides × side length P = 5 × 3.2 cm Step 3: Calculate the perimeter. P = 16.0 cm The perimeter of the pentagon is: 16.0 cm 2. Calculate the surface area of the rectangular prism. Step 1: Identify the dimensions of the rectangular prism. Length l = 7 cm Width w = 2 cm Height h = 3 cm Step 2: Use the formula for the surface area of a rectangular prism. Surface Area (SA) = 2(lw + lh + wh) Step 3: Substitute the dimensions into the formula and calculate. SA = 2((7 cm × 2 cm) + (7 cm × 3 cm) + (2 cm × 3 cm)) SA = 2(14 cm^2 + 21 cm^2 + 6 cm^2) SA = 2(41 cm^2) SA = 82 cm^2 The surface area of the rectangular prism is: 82 cm^2 3. Calculate surface area of the open cylinder. Use = 3.14. Step 1: Identify the given values and ensure consistent units. Radius r = 50 cm Height h = 1.2 m Convert height to centimeters: h = 1.2 m × 100 cm/m = 120 cm Use = 3.14. Step 2: Determine the formula for the surface area of an open cylinder. An open cylinder has one circular base and a curved surface, but no top. Surface Area (SA) = Area of base + Area of curved surface SA = r^2 + 2 rh Step 3: Substitute the values into the formula. SA = (3.14 × (50 cm)^2) + (2 × 3.14 × 50 cm × 120 cm) Step 4: Calculate the area of the base. Area of base = 3.14 × 2500 cm^2 = 7850 cm^2 Step 5: Calculate the area of the curved surface. Area of curved surface = 2 × 3.14 × 50 × 120 cm^2 Area of curved surface = 3.14 × 100 × 120 cm^2 Area of curved surface = 3.14 × 12000 cm^2 = 37680 cm^2 Step 6: Add the areas to find the total surface area. SA = 7850 cm^2 + 37680 cm^2 SA = 45530 cm^2 The surface area of the open cylinder is: 45530 cm^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.