Determine the radius of the base of the cone.

The cone has a slant height $L = 7\,\text{cm}$ and a vertex angle of $60^\circ$.
Consider the isosceles triangle formed by the slant heights and the diameter of the base. Since the two equal sides are $7\,\text{cm}$ and the angle between them is $60^\circ$, this is an equilateral triangle.
Therefore, the diameter of the base is $7\,\text{cm}$.
The radius of the base $r = \frac{\text{diameter}}{2} = \frac{7}{2}\,\text{cm} = 3.5\,\text{cm}$.

The radius of the sector is the slant height $L = 7\,\text{cm}$.
The arc length of the sector is equal to the circumference of the base circle.
Circumference $C = 2\pi r = 2\pi (3.5\,\text{cm}) = 7\pi\,\text{cm}$.
The angle $\theta$ of the sector (in degrees) is given by the formula:

The net of the cone consists of two parts:

• A circular base with a radius of $3.5\,\text{cm}$.
• A sector of a circle with a radius of $7\,\text{cm}$ and an angle of $180^\circ$ (a semicircle).

40) Maureen tossed a die once. Determine the probability that she obtained an even number.

When a standard die is tossed once, the possible outcomes are the integers from 1 to 6.
The sample space $S = \{1, 2, 3, 4, 5, 6\}$.
The total number of possible outcomes is $n(S) = 6$.

We are looking for the probability of obtaining an even number. The even numbers in the sample space are $\{2, 4, 6\}$.
The number of favorable outcomes is $n(E) = 3$.

The probability $P(E)$ of an event $E$ is given by the formula:

The probability that she obtained an even number is $\frac{1}{2}$.