Explain how you could convert 152 cups to gallons
1 answer:
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The volume of the composite figure is the third option 385.17 cubic centimeters.
Step-by-step explanation:
Step 1:
The composite figure consists of a cone and a half-sphere on top.
We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.
The radius is 4 cm and the height is 15 cm.
The volume of the cone :
cubic cm.
Step 3:
The area of a half-sphere is half of a full sphere.
The volume of a sphere is given by multiplying with π and the cube of the radius (r³).
Here the radius is 4 cm. We take π as 3.1415.
The volume of a full sphere cubic cm.
The volume of the half-sphere cubic cm.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume cub cm. This is closest to the third option 385.17 cubic centimeters.
An equation of the form ax+by+c=0, where x, y are variable, and a, b, c are numbers, is called a "linear equation"
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
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-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
-------------------------------------------------------------------------------------------------
-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.