Respuesta :
Answer:
(- 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
