To solve this problem, we will compute the lateral surface area and volume of the hemisphere. The radius is given as 7.08 units. Let's calculate:

1. Lateral Surface Area of a Hemisphere

The lateral surface area of a hemisphere is calculated as: $A = 2 \pi r^2$ Where:

• $r = 7.08$

Substitute $r = 7.08$: $A = 2 \pi (7.08)^2$

$A = 2 \pi (50.1264) \approx 2 \times 3.1416 \times 50.1264$

$A \approx 314.9 \ \text{(rounded to the nearest whole number)}.$

So, the lateral surface area is 315 units².

2. Volume of the Hemisphere

The volume of a hemisphere is: $V = \frac{2}{3} \pi r^3$

Substitute $r = 7.08$: $V = \frac{2}{3} \pi (7.08)^3$

$V = \frac{2}{3} \pi (354.084) \approx \frac{2}{3} \times 3.1416 \times 354.084$

$V \approx 741.78 \ \text{(rounded to the nearest whole number)}.$

So, the volume is 742 units³.

Final Answers:

1. Lateral Surface Area: $\mathbf{315 \, \text{units}^2}$
2. Volume: $\mathbf{742 \, \text{units}^3}$

Let me know if you'd like more details or further assistance!

5 Related Questions:

1. How do you calculate the total surface area of a hemisphere?
2. What is the difference between the lateral surface area and the total surface area of a hemisphere?
3. How would the lateral surface area change if the radius doubled?
4. What formula do you use for the volume of a full sphere?
5. How is the calculation of lateral surface area different for a cone?

Tip:

Always double-check the rounding rules when working with π to ensure precision in your calculations!