1、 Cone A has volume 24. When its radius and height are multiplied by the same factor, the cone’s surface area doubles. What is Cone A’s new volume?
(A)
(B)48
(C)
(D)96
(E)Not enough information to tell
2、 Arectangle stands so that its 6 inch side lies flat against the ground. If
the rectangle is rotated around the axis of one of its two 4 inch sides, what is the volume of the resulting cylinder?
(A)24?€
(B)36?€
(C)64?€
(D)96?€
(D)144?€
Answers
1、 C
The formula for a cone‘s surface area is πr2 + πrl. A cone‘s volume is 1/ 3πr2h. So if the dimensions of a cone are multiplied by the same factor, a,
then its surface area multiplies by the square of that factor. If the dimensions of a cone are multiplied by the same factor, the volume becomes multiplied by the cube of that
factor:
In general, for solids, if each dimension of a cone is multiplied by the same factor, the solid‘s surface area is multiplied by the square of that factor, and its volume increases by the cube of that factor. If the surface area of Cone A doubles, its dimensions are multiplied by a factor of Thus, the cone‘s volume is multiplied by a factor of Cone A‘s
new volume is
2、 E
If the rectangle is rotated about a side of length 4, then the height of the cylinder will be 4 and the radius will be 6.
Once you visualize the cylinder, you can plug in the values for the volume of a cylinder:
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