Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of h = 6 m when its radius decreases from r = 14 m to r = 13.9 m (S= (pi)(r)sqrt(r^2+h^2)? S = __ ?

(- 42.8π/√232)m²

Step-by-step explanation:

For any function, y = f(x), we approximately from a to a + ∆x

We can make use of the formula

∆y = f'(a)∆x

Where S = πr√(r² + h²)

We are asked to find S

h = 6m

r = decreases from 14m to 13.9

S = d/dr[ πr√(r² + h²)] ×(13.9 - 14)

Where h = 36m

S = π d/dr [ r √(r² + 6²)] × (13.9 - 14)

S = π d/dr [ r √(r² + 36)] × (13.9 - 14)

Where r = 14m

S = π [√(r² + 36) + r²/√(r² + 36)] × (13.9 - 14)

S = π [√(14²+ 36) + 14²/√(14² + 36)] × (13.9 - 14)

S = π [√(196+ 36) + 196/√(196 + 36)] × (13.9 - 14)

S = π[√232 + 196/√232] × (13.9 - 14)

S = π × - 0. 1 [√232 + 196/√232]

Collecting like terms

S = π × - 0. 1 × 1/√232 [232 + 196]

S = π × - 0. 1 × 1/√232[428]

S =(- 42.8π/√232)m²

you have to put the graph on here with the question

step-by-step explanation:

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: