Let's approach each part of the question step-by-step.
### Problem 4: Regular polygon with an exterior angle of 60 degrees
The formula to calculate the exterior angle of a regular polygon is:
\(\[ \text{Exterior angle} = \frac{360^\circ}{n} \]\)
where \(\( n \)\) is the number of sides of the polygon. We need to find the polygon with an exterior angle measuring 60 degrees.
Given:
\(\[ \text{Exterior angle} = 60^\circ \]\)
Using the formula:
\(\[ 60 = \frac{360}{n} \]\)
To find \(\( n \)\):
\(\[ n = \frac{360}{60} \]\)
\(\[ n = 6 \]\)
A regular polygon with 6 sides is a regular hexagon.
Therefore, the answer is:
B. Regular hexagon
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### Problem 5: Volume of a sphere with a radius of 30 cm
The formula to calculate the volume of a sphere is:
\(\[ \text{Volume} = \frac{4}{3} \pi r^3 \]\)
where \(\( r \)\) is the radius of the sphere. Given that the radius \(\( r = 30 \)\) cm, we can plug this value into the formula.
\(\[ \text{Volume} = \frac{4}{3} \pi (30)^3 \]\)
Now, let's calculate it step-by-step:
1. Calculate \(\( 30^3 \)\):
\(\[ 30^3 = 30 \times 30 \times 30 = 27000 \]\)
2. Multiply by \(\( \frac{4}{3} \)\):
\(\[ \frac{4}{3} \times 27000 = \frac{108000}{3} = 36000 \]\)
3. Multiply by \(\( \pi \)\) (approximately \(\( 3.14159 \)\)):
\(\[ 36000 \times 3.14159 \approx 113097.24 \]\)
4. Round to the nearest whole number:
\(\[ 113097.24 \approx 113097 \]\)
Therefore, the volume of the sphere to the nearest whole number is:
113097 cm³
