Find the volume of the figure if the radius of the hemisphere and cylinder is 6 inches and the height of the cylinder is 12 inch
1 answer:
Answer: Option B
Step-by-step explanation:
The formula for calculate the volume of a hemisphere is:
Where r is the radius:
The formula for calculate the volume of a cylinder is:
Where r is the radius and h is the height.
Therefore, the volume of the figure is the sum of the volume of the hemisphere and the volume of the cylinder.
Finally, knowing that the radius of the hemisphere and the cylinder is 6 inches and the height of the cylinder is 12 inches, you can substitute values. Then:
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We have to find the" ratio of the area of sector ABC to the area of sector DBE".
Now,
the general formula for the area of sector is
Area of sector= 1/2 r²θ
where r is the radius and θ is the central angle in radian.
180°= π rad
1° = π/180 rad
For sector ABC, area= 1/2 (2r)²(β°)
= 1/2 *4r²*(π/180 β)
= 2r²(π/180 β)
For sector DBE, area= 1/2 (r)²(3β°)
= 1/2 *r²*3(π/180 β)
= 3/2 r²(π/180 β)
Now ratio,
Area of sector ABC/Area of sector DBE =
= 4/3
Greetings!
FOIL stands for:
Front
Outside
Inside
Last
This tells which terms to multiply when using the Distributive Property.
(NOTE: Only applicable with 2-term Polynomials)
For Example:
Multiply the Fronts of both Equations:
Multiply the Outsides of both Equations:
Multiply the Insides of both Equations:
Multiply the Lasts of both Equations:
Simplify.
Alternative Method (My Prefered Method)
Use Regular Distributive Property.
Simplify.
Hope this helps.
-Benjamin
FOIL stands for:
Front
Outside
Inside
Last
This tells which terms to multiply when using the Distributive Property.
(NOTE: Only applicable with 2-term Polynomials)
For Example:
Multiply the Fronts of both Equations:
Multiply the Outsides of both Equations:
Multiply the Insides of both Equations:
Multiply the Lasts of both Equations:
Simplify.
Alternative Method (My Prefered Method)
Use Regular Distributive Property.
Simplify.
Hope this helps.
-Benjamin