Final answer:
The diameter of the coffee mug is approximately 9 cm.
Step-by-step explanation:
To find the diameter of the coffee mug, we can use the given information. Let's assume the diameter of the mug is d. According to the design specifications, the height of the mug is 1.5 times its diameter, so the height would be 1.5d. The formula for the volume of a cylindrical mug is V = πr^2h, where r is the radius and h is the height. Since the capacity of the mug is 450 ml, we can set up the equation 450 = π(d/2)^2 * 1.5d.
Simplifying the equation, we get 450 = (3.1416)(d^2/4)(1.5d). Multiplying all the terms, we find 450 = 0.7854d^3. Dividing both sides by 0.7854, we get d^3 = 573.3636. Taking the cube root of both sides, we find d ≈ 8.967 cm. Therefore, the diameter of the coffee mug is approximately 9 cm.