Let's solve the problem step-by-step to find the surface area of a right cone given its slant height (7 units) and radius (5 units).
1. Identify the components of the surface area:
- The surface area of a cone is the sum of its lateral surface area and the base surface area.
2. Calculate the lateral surface area:
- The formula for the lateral surface area of a cone is [tex]\( \pi \cdot r \cdot l \)[/tex],
where [tex]\( r \)[/tex] is the radius and [tex]\( l \)[/tex] is the slant height.
- Given [tex]\( r = 5 \)[/tex] and [tex]\( l = 7 \)[/tex], we have:
[tex]\[
\text{Lateral Surface Area} = \pi \cdot 5 \cdot 7 = 35\pi
\][/tex]
3. Calculate the base surface area:
- The formula for the base surface area of a cone is [tex]\( \pi \cdot r^2 \)[/tex],
where [tex]\( r \)[/tex] is the radius.
- Given [tex]\( r = 5 \)[/tex], we have:
[tex]\[
\text{Base Surface Area} = \pi \cdot 5^2 = \pi \cdot 25 = 25\pi
\][/tex]
4. Calculate the total surface area:
- The total surface area is the sum of the lateral surface area and the base surface area.
- Therefore,
[tex]\[
\text{Total Surface Area} = 35\pi + 25\pi = 60\pi
\][/tex]
Thus, the total surface area of the cone is [tex]\( 60\pi \)[/tex] units². The correct answer is:
B. [tex]\( 60\pi \)[/tex] units²
