CBSE Class 10-Mathematics: Chapter –13 Surface Areas and Volumes Part 2

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Question 6:

A cylindrical vessel of diameter and height is fixed symmetrically inside a similar vessel of diameter and height . The total space between two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required?

Answer:

Volume of cork dust required

Question 7:

A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.

Answer:

Volume of building

height of building

Question 8:

The height of the cone is A small cone is cut of at the top by a plane parallel to its base if its volume be of the volume of the given cone at what height above the base is the section cut.

Answer:

of cone

The height of the cone

The Height of the Cone

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height at which section is made

Question 9:

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is of the curved surface of the whole cone, find the ratio of the line segments into which the cone’s altitude is divided by the plane.

Answer:

We know that

C. SA of frustum

The height of the cone

The Height of the Cone

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On simplifying we get

Required ratios