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Volume of a Frustum

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Question 5
Write ‘True’ or ‘False’ and justify your answer in the following
The volume of the frustum of a cone is $\frac{1}{3} π h [r_{1}^{2} + r_{2}^{2} - r_{1} r_{2}]$ , where h is vertical height of the frustum and
$r_{1}, r_{2}$ are the radii of the ends.

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Solution

The given statement is false.
Since, the volume of the frustum of a cone is $\frac{1}{3} π h [r_{1}^{2} + r_{2}^{2} + r_{1} r_{2}]$ where h is vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.
In below figure $r = r_{1} a n d R = r_{2}$

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Q. State True(1) or False(0).

The volume of the frustum of a cone is

\frac{1}{3} π h [r_{1}^{2} r_{2}^{2} - r_{1} r_{2}],

where h is vertical
height of the frustum and

r_{1}, r_{2}

are the radii of the ends.

Q. Question 7
The curved surface area of a frustum of a cone is

π (r_{1} + r_{2}) l

l = \sqrt{h^{2} + (r_{1} + r_{2})^{2}}

r_{1} a n d r_{2}

are the radii of the two ends of the frustum and h is the vertical height.

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Q. State True(1) or False(0).

The curved surface area of a frustum of a cone is

π l (r_{1} + r_{2})

l = \sqrt{h^{2} + {(r_{1} - r_{2})}_{1}^{2}}

r_{1} a n d r_{2}

are the radii of the two ends of the frustum and

h

is the vertical height.

Q. Consider a frustum of cone with larger and smaller radius equal to

r_{1} a n d r_{2}

, respectively. Then, volume of frustum of a cone is

\frac{1}{3} π h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2})

.

State whether the statement is True or False.

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Volume of a Frustum

Standard X Mathematics

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