Question

the graph shows the relationship between the total surface area A of a square pyramid with a fixed base and its slant height s. Estimate the slant height if the surface area is 100m^2

Answer 1

The slant height if the surface area is 100 meter squared is 3.57 meters

Estimating the slant height given the surface area

From the question, we have the following parameters that can be used in our computation:

The graph

This graph is a linear function and can be represented as

y = mx + c

Where c is the y-intercept

From the graph, the y-intercept is 50

So, we have

y = mx + 50

Using the point (5, 120), we have

5m + 50 = 120

5m = 70

m = 14

Recall that

y = mx + 50

So, we have

y = 14x + 50

When the surface area is 100, we have

14x + 50 = 100

14x = 50

Divide by 14

x = 3.57

Hence, the slant height is 3.57 meters