The answer to the question is d
The volume of the cylinder is:
V = pi * r ^ 2 * h = 64
The surface area is:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
We write the area as a function of r:
A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
Rewriting:
A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
A (r) = 2 * pi * r ^ 2 + 128 / r
Deriving:
A '(r) = 4 * pi * r - 128 / r ^ 2
We equal zero and clear r:
0 = 4 * pi * r - 128 / r ^ 2
128 / r ^ 2 = 4 * pi * r
r ^ 3 = 128 / (4 * pi)
r = (128 / (4 * pi)) ^ (1/3)
r = 2.17 cm
The height is:
h = 64 / (pi * r ^ 2)
h = 64 / (pi * (2.17) ^ 2)
h = 4.33 cm
Answer:
The dimensions giving the minimum surface area are:
r = 2.17 cm
h = 4.33 cm
Answer:
in my panies
Step-by-step explanation:
Answer: £1632
Step-by-step explanation:
SI = prt
SI = 1500 x 0.022 x 4
SI = 132
After 4 years, he will have
1500 + 132 = 1632
Answer:
π − 2
Step-by-step explanation:
Graph of the region:
desmos.com/calculator/pcascl0frf
If we integrate with respect to x:
∫₀² (y − 0) dx
∫₀² sin⁻¹(x/2) dx
But we want to integrate with respect to y. Let's start by finding the new limits of integration.
y = sin⁻¹(x/2), so when x = 0, y = 0. When x = 2, y = π/2.
Next, we need to find x in terms of y.
sin y = x/2
x = 2 sin y
So the integral with respect to y is:
∫₀ᵖⁱ² (2 − x) dy
∫₀ᵖⁱ² (2 − 2 sin y) dy
Integrating:
(2y + 2 cos y + C) |₀ᵖⁱ²
(π + 2 cos (π/2) + C) − (0 + 2 cos 0 + C)
(π + 0 + C) − (0 + 2 + C)
π − 2
