The net of a cylinder is shown below.a) Work out the length x, in mm. b) What is the total surface area of the cylinder, in mm²? Give your answers in terms of . 5 mm 5 mm X 3 mm Not drawn accurately

(a) The length of x is x = 10π mm. (b) The area of the net cylinder is A = 80π mm². Given information: The radius of the sphere is 5 mm. (a) To find the value of x: The value of x is described as the circumference of the sphere. So, x = 2πr Here, r = 5 mm. x = 2π(5) x = 10π mm. (b) To find the area of the net cylinder, use the formula described below, A = 2πr² + hx. Here, h = 3 mm, and x = 10π. A = 2π(5)² + (3)(10π) A = 50π + 30π A = 80π mm². To learn more about the cylinder; brainly.com/question/16134180 #SPJ1

Final answer: The length x is equal to 5/π mm. The total surface area of the cylinder is 55/2π mm². Explanation: The net of a cylinder is formed by the following shapes: a rectangle and two circles. a) Length x can be determined by finding the circumference of the circle and subtracting the length of the rectangle. The circumference of a circle is given by the formula: C = 2πr, where r is the radius. In this case, the circumference is equal to the length of the rectangle, so we have the equation: 2πr = 5 mm. Solving for r, we get r = 5/(2π) mm. Therefore, the length x is twice the radius of the circle, which is 2 × 5/(2π) = 5/π mm. b) To find the surface area of the cylinder, we need to calculate the areas of the two circles (A = πr²) and the area of the rectangle (A = l × w, where l is the length and w is the width). The length of the rectangle is x and the width is 3 mm. The total surface area is the sum of these three areas, so we have: 2πr² + x × 3. We can substitute the value of x in terms of π that we found in part a, and simplify the equation to get the total surface area in terms of π: 2π(5/(2π))² + (5/π) × 3 = 25/2π + 15/π = 55/2π mm². Learn more about Cylinder here: brainly.com/question/3216899 #SPJ12