Answer:
Volume: 
Ratio: 
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so 
. Moreover, we have to add the surface of the base, which is 
. So the total surface area of the hemispherical tank is
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
Answer:
51 m^2
Step-by-step explanation:
The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.
The applicable formulas are ...
area of a triangle:
A = (1/2)bh
area of a rectangle:
A = bh
area of a trapezoid:
A = (1/2)(b1 +b2)h
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We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...
A = (1/2)(16 m + 10 m)(5 m) = 65 m^2
The area of the white internal rectangle is ...
A = (2 m)(7 m) = 14 m^2
So, the shaded area is the difference:
65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure
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<em>Alternate approach</em>
Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...
(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2
= 51 m^2
The product of these numbers are 0.100
since 0.100 is same as 0.1
so there is only one decimal place
COMMON SENSE
Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
4 since she can’t make half a costume for a kid (so not 4.5)
