To find the lateral surface area and surface area of a cone, we’ll use the following formulas:

Given values

• Slant height (l) = 8 m
• Radius (r) = 5 m
• Pi (π) = 3.14

Formulas

1. Lateral Surface Area (LSA) of a cone = π * r * l
2. Total Surface Area (TSA) of a cone = LSA + Area of the base = π * r * (l + r)

Let's substitute these values:

(a) Lateral Surface Area

$\text{LSA} = \pi \times r \times l = 3.14 \times 5 \times 8 = 125.6 \text{ m}^2$

(b) Total Surface Area

$\text{TSA} = \pi \times r \times (l + r) = 3.14 \times 5 \times (8 + 5) = 3.14 \times 5 \times 13 = 204.1 \text{ m}^2$

Answers

1. Lateral Surface Area = 125.6 m²
2. Surface Area = 204.1 m²

Would you like further explanation or have any other questions?

Here are five related questions you might find interesting:

1. What is the volume of a cone with the same dimensions?
2. How would the surface area change if the radius were doubled?
3. Can you calculate the lateral surface area if only the height of the cone (not the slant height) is given?
4. How does the surface area formula differ for a cylinder compared to a cone?
5. What is the surface area of a cone with a slant height that is 1.5 times the radius?

Tip: Always double-check units to ensure consistency in your calculations!