1. Decide which for mula to use. 2. Identify the information you are given. 3. Substitute for your variables. 4. Answer the question - evaluate the expression. $$ S A=\frac{1}{2} l p+B $$ $$ S A=\pi r^{2}+\pi r l $$

Question

UpStudy AI · Accepted Answer

**Step 1. Decide Which Formula to Use**  
We have two formulas provided:  
- $$ SA = \frac{1}{2} l p + B $$  
- $$ SA = \pi r^{2} + \pi r l $$

Choose the proper formula based on the solid you are analyzing. For example:  
- If you are finding the surface area of a pyramid (or another polygonal solid) with base area $$ B $$, lateral edge length $$ l $$, and base perimeter $$ p $$, use  
  $$
  SA = \frac{1}{2} l p + B.
  $$  
- If you are finding the surface area of a cone, with base radius $$ r $$ and slant height $$ l $$, use  
  $$
  SA = \pi r^{2} + \pi r l.
  $$

---

**Step 2. Identify the Information You Are Given**  
Determine which values are provided in your problem statement. For example:  
- In the polygonal solid case, you might be given:  
  - Base area: $$ B $$  
  - Lateral edge (or slant height): $$ l $$  
  - Base perimeter: $$ p $$  
- In the cone case, you might be given:  
  - Radius: $$ r $$  
  - Slant height: $$ l $$

Make sure that all the necessary dimensions required by the formula are known or can be computed.

---

**Step 3. Substitute for Your Variables**  
Once you have the numerical values, substitute them into the chosen formula. For instance, if you are using the cone surface area formula and are given:  
- $$ r = 3 $$  
- $$ l = 5 $$

Then substitute into the formula:  
$$
SA = \pi (3)^{2} + \pi (3)(5).
$$

---

**Step 4. Evaluate the Expression**  
Now, simplify and compute the value. Continuing with our cone example:

1. Square the radius:  
   $$
   3^{2} = 9.
   $$
2. Substitute into the expression:  
   $$
   SA = 9\pi + 15\pi.
   $$
3. Combine like terms:  
   $$
   SA = (9 + 15)\pi = 24\pi.
   $$

Thus, the surface area is  
$$
SA = 24\pi.
$$

Follow these steps with your given values and the appropriate formula to solve your specific problem.
**Steps to Find Surface Area:** 1. **Choose the Right Formula:** - For a pyramid or polygonal solid: $$ SA = \frac{1}{2} l p + B $$. - For a cone: $$ SA = \pi r^{2} + \pi r l $$. 2. **Identify Given Information:** - List all known values like base area $$ B $$, base perimeter $$ p $$, lateral edge $$ l $$, radius $$ r $$, and slant height $$ l $$. 3. **Substitute Values into the Formula:** - Plug the known values into the chosen formula. 4. **Calculate the Surface Area:** - Perform the calculations to find the final surface area value. Use these steps to determine the surface area based on the given information and the appropriate formula.

1. Decide which for mula to use. 2. Identify the information you are given. 3. Substitute for your variables. 4. Answer the question - evaluate the expression. \( S A=\frac{1}{2} l p+B \) \( S A=\pi r^{2}+\pi r l \)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Geometry Questions