Question

1. find the surface area of the cone in terms of π.

Explanation:

Step1: Identify cone parameters

Radius $r = 7 \, \text{cm}$, slant height $l = 10 \, \text{cm}$

Step2: Calculate lateral surface area

$LSA = \pi r l = \pi \times 7 \times 10 = 70\pi$

Step3: Calculate base area

$Base = \pi r^2 = \pi \times 7^2 = 49\pi$

Step4: Total surface area

$TSA = LSA + Base = 70\pi + 49\pi = 119\pi$

Wait correction: Wait no—wait the diagram shows the diameter as 7cm? Wait no, the line is labeled 7cm: if it's diameter, radius is 3.5cm. Wait no, the problem says "surface area of the cone"—standard formula is $\pi r l + \pi r^2$. Wait maybe the 7cm is radius? Wait no, let's check again: the diagram has a dashed line from center to edge labeled 7cm (radius) and slant height 10cm. Then lateral area is $\pi*7*10=70\pi$, base area $\pi*7^2=49\pi$, total $119\pi$. Yes, that's correct. My initial correction was wrong—7cm is radius. So final answer is $119\pi$.

Step1: Identify cone parameters

Radius $r=7\,\text{cm}$, slant height $l=10\,\text{cm}$

Step2: Compute lateral surface area

$LSA = \pi r l = \pi \times 7 \times 10 = 70\pi$

Step3: Compute base area

$Base = \pi r^2 = \pi \times 7^2 = 49\pi$

Step4: Sum for total surface area

$TSA = 70\pi + 49\pi = 119\pi$

Answer:

$85\pi \, \text{cm}^2$