CBSE Class 10-Mathematics: Chapter –13 Surface Areas and Volumes Part 3

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Question 10:

Two right circular cones are made having times the radius of Y and Yhaving half the volume of . Calculate the ratio of heights of .


Let radius of cone

Radius of Cone

Question 11:

If the areas of three adjacent faces of cuboid are respectively, find the volume of the cuboids.


Volume of cuboid

Questions 12:

A shuttlecock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameters of the frustum are , and the height of the entire shuttlecock is . Find the external surface area.


of lower end of frustum

of upper end

of frustum

External surface area of shuttlecock

On substituting we get,

Question 13:

A conical vessel of radius and height is filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in the figure. What fraction of water flows out?


This problem can be done in many ways

Let “r” be the radius of sphere

In right triangle

Volume of that flows out of cone volume of sphere

Fraction of water overflows

Question 14:

A golf ball has a diameter equal to . Its surface has dimples each of radius . Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical


of ball

TSA exposed to surroundings