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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Here are the solutions to your math questions: 1. Area of a triangle Step 1: Recall the formula for the area of a triangle. The area of a triangle is given by: A = (1)/(2) × base × height Step 2: Substitute the given values into the formula. Given base = 18 cm and height = 7 cm. A = (1)/(2) × 18 cm × 7 cm Step 3: Calculate the area. A = 9 cm × 7 cm A = 63 cm^2 The area of the triangle is 63 cm^2. 2. Perimeter of a circle Step 1: Recall the formula for the perimeter (circumference) of a circle. The circumference of a circle is given by: C = 2 r where r is the radius. Step 2: Substitute the given radius into the formula. Given radius r = 5 cm. C = 2 × × 5 cm Step 3: Calculate the circumference. C = 10 cm Using ≈ 3.14159: C ≈ 10 × 3.14159 cm C ≈ 31.4159 cm The perimeter of the circle is 10 cm ≈ 31.42 cm. 3. Area of a circle Step 1: Recall the formula for the area of a circle. The area of a circle is given by: A = r^2 where r is the radius. Step 2: Substitute the given radius into the formula. Given radius r = 6 cm. A = × (6 cm)^2 Step 3: Calculate the area. A = × 36 cm^2 A = 36 cm^2 Using ≈ 3.14159: A ≈ 36 × 3.14159 cm^2 A ≈ 113.097 cm^2 The area of the circle is 36 cm^2 ≈ 113.10 cm^2. 4. Volume for each of the cubes Step 1: Recall the formula for the volume of a cube. The volume of a cube is given by: V = edge length^3 a) Edge length 2 cm Step 2: Substitute the edge length into the formula. V = (2 cm)^3 Step 3: Calculate the volume. V = 2 cm × 2 cm × 2 cm V = 8 cm^3 The volume of the cube is 8 cm^3. b) Edge length 4 cm Step 2: Substitute the edge length into the formula. V = (4 cm)^3 Step 3: Calculate the volume. V = 4 cm × 4 cm × 4 cm V = 64 cm^3 The volume of the cube is 64 cm^3. 5. Area of a square Step 1: Recall the formula for the area of a square. The area of a square is given by: A = side length^2 Step 2: Substitute the given side length into the formula. Given side length = 3 cm. A = (3 cm)^2 Step 3: Calculate the area. A = 3 cm × 3 cm A = 9 cm^2 The area of the square is 9 cm^2. That's 2 down. 3 left today — send the next one.