### Introduction:

Are you struggling with understanding the answers to Lesson 18 Homework 3.5? Do you find yourself grappling with some of the concepts covered in this lesson? If so, fear not! In this blog post, we will thoroughly dissect the Lesson 18 Homework 3.5 answer key, breaking down each question in a simplified manner. Our objective is to empower you with a clear grasp of each topic covered, enabling you to confidently conquer your homework and enhance your comprehension of the subject.

### Question 1: Calculating Sphere Volume and Surface Area

The first question tasks you with calculating the volume and surface area of a sphere with a radius of 5cm. To solve this, we utilize the formulas V = 4/3πr^3 and SA = 4πr^2. Plugging in the radius value, we obtain a volume of 523.6cm^3 and a surface area of 314.16cm^2.

### Question 2: Finding the Hypotenuse of a Right Triangle

In the second question, you’re prompted to determine the hypotenuse of a right triangle with legs measuring 3cm and 4cm. The Pythagorean theorem, c^2 = a^2 + b^2, comes to the rescue. Plugging in the leg values, 3 and 4, we deduce the hypotenuse to be 5cm.

### Question 3: Grasping Simple Interest

The third question delves into the concept of simple interest. Armed with the principal amount, interest rate, and loan duration, we employ the formula I = Prt, where I signifies interest, P is principal, r stands for rate, and t denotes time. By inputting the given values – a principal of $10,000, an interest rate of 5%, and a time of 5 years – we calculate an interest of $750.

### Question 4: Mastering the Distance Formula

Question four revolves around the distance formula, instrumental for determining the gap between two points on a coordinate plane. Armed with the points (-3, 4) and (1, -2), we plug them into the formula d = sqrt((x2 – x1)^2 + (y2 – y1)^2). The outcome reveals a distance of 6.32 units.

### Question 5: Unveiling Slope Secrets

The fifth question delves into slope comprehension. Armed with the points (2, 3) and (5, 7), your task is to unveil the slope of the line passing through these points. Employing the formula m = (y2 – y1) / (x2 – x1), we obtain a slope of 1.33.

### Conclusion:

In summary, we sincerely hope that this comprehensive breakdown of the Lesson 18 Homework 3.5 answer key has provided you with a deeper understanding of the concepts tackled in each question. Remember, mathematics can indeed pose challenges, but with persistent practice and unwavering patience, success is within your grasp. Should any portions remain perplexing or intricate, don’t hesitate to seek additional assistance. Keep honing your skills, and may the odds be ever in your favor!