All SAT Math Resources
Example Questions
Example Question #7 :How To Find The Volume Of A Cone
找到的体积cone with radius 3 and height 5.
To solve, simply use the formula for the volume of a cone. Thus,
To remember the formula for volume of a cone, it helps to break it up into it's base and height. The base is a circle and the height is just h. Now, just multiplying those two together would give you the formula of a cylinder (see problem 3 in this set). So, our formula is going to have to be just a portion of that. Similarly to volume of a pyramid, that fraction is one third.
Example Question #8 :How To Find The Volume Of A Cone
Find the area of a cone whose radius is 4 and height is 3.
To solve, simply use the formula for the area of a cone. Thus,
Example Question #9 :How To Find The Volume Of A Cone
The volume of a right circular cone is. If the cone's height is equal to its radius, what is the radius of the cone?
The volume of a right circular cone with radiusand heightis given by:
Since the height of this cone is equal to its radius, we can say:
Now, we can substitute our given volume into the equation and solve for our radius.
Example Question #10 :How To Find The Volume Of A Cone
The above is a right circular cone. Give its volume.
The volume of a right circular conecan be calculated from its heightand the radiusof its base using the formula
.
We are given, but not.
,, and the slant heightof a right circular cone are related by the Pythagorean Theorem:
Settingand, substitute and solve for:
Taking the square root of both sides and simplifying the radical:
Now, substitute forandand evaluate:
Example Question #181 :Solid Geometry
The above is a right circular cone. Give its volume.
The volume of a right circular conecan be calculated from its heightand the radiusof its base using the formula
.
and,所以替代品和评估:
Example Question #12 :Cones
In terms of, express the volumeof the above right circular cone.
The volumeof a cone can be calculated from its heightand the radiusof its base using the formula
The slant heightis shown in the diagram to be 24. By the Pythagorean Theorem,
Settingand solving for:
Substituting in the volume formula for:
.
Example Question #11 :Cones
In terms of, express the volumeof the provided right circular cone.
The volumeof a cone can be calculated from its heightand the radiusof its base using the formula
The height of the cone is shown to be equal to 20, so substituting accordingly: