Lesson: Chapter - 7

Explanations

1.C

The length of the diagonal doubles, just like the rectangular solid’s other dimensions.

The formula for the length of the diagonal of a rectangular solid is wherel, w, and hare the dimensions of the solid. Substitute 2 l,2w, and2h for these values:

2.D

The volume of a cylinder is given by the formula pr²h. In the case of this cylinder, the radius is equal to height (r = h), so

With the information given by the question, we can find the radius by setting either4pr² = 100porr² =100p/4p= 25. Either way, the radius of the cylinder works out to 5, which means that the volume of the cylinder isp5³ =125p.

3.C

The formula for a cone’s surface area ispr² +p rl. A cone’s volume is ¹/ ₃pr²h. So if the dimensions of a cone are multiplied by the same factor, a,

p (ar)² + p (ar)(al) = p a²r² + p a²r l = a²(p r²+ p rl)

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 v2 Thus, the cone’s volume is multiplied by a factor of (v2)³ = 2 v2. Cone A’s new volume is 24 × (2v2) = 48 v2.

4.E

If the rectangle is rotated about a side of length 4,then the height of the cylinder will be 4and the radius will be 6.

Once you visualize the cylinder, you can plug in the values for the volume of a cylinder:t× 6²× 4 = 144p

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Mathematics Practice Questions