Answer:
a)1.414 cm/min
b)14.14 cm/min
Step-by-step explanation:
Volume of a cone can be determined by the formula i.e
V= 1/3 πr²h
where, 'h'is height and 'r' is radius
Now, when height and radius of shallow concrete conical reservoir is,
r= 50m = 5000cm
h= 5m = 500cm
As height and radius are proportional, we can write
h= ⇒ r= 10h
As the water is flowing and filling up reservoir at the rate of 40 m³/min
So,
40 x cm³/min
a) in this part, we have to find and the height given is:
height 'h'= 3m=> 300m
Therefore,
V= 1/3 πr²h => 1/3 π (10h)² h
V= 100 π h³/ 3
π 3h²
40 x = π300²
= 40 x / (100 x 300²)π
= 1.414 cm/min
b) in this part, we need to find how fast is the radius of the water's surface changing i.e
We have h=300 cm . therefore, r= 10h => 10(300)
r= 3000
V= 1/3 πr²h =>1/3 πr²
V= 1/30 πr³
Applying Derivation both side w.r.t to 't'
π 3r²
40 x = 1/10 π (3000)²
= 40 x x 10 / π (3000)²
= 14.14 cm/min
Thus, the radius of the water's surface is changing at the rate of 14.14 cm/min
Answer:
2x + 6 = 10
x = 2
Step-by-step explanation:
2x + 6 = 10
2x = 4
x = 2
The smallest possible measure of angle h is 90 degrees. Since f and g are complementary angles ( add up to 90 degrees), the h has to at minimum be 90 degrees to equal 180 degrees (supplementary angles).
Answer:
Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77
Step-by-step explanation:
The given dimensions are
Width of the rectangle is 6inches.
Length of the rectangle 10inches.
Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.
so lets consider two cases
CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder
2*pi*r = 6
r =
r = Inch
and the height = 10inch.
Volume of the resultant cylinder will be
=
=
=
= = 28.662
CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.
2*pi*r= 10
r =
and the height of the cylinder is 6 inch
Now the volume of the cylinder will be
Volume=
=
=
= = 47.77
Clearly we have the second case in which the resulting Cylinder will have the maximum volume.
Therefore the CASE-2 will provide the maximum Volume of 47.77 to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.