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UPSKILL MATH PLUS

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Subjects
Mathematics State Board
Class 10
Mensuration
Volume of a Sphere, Hollow Sphere, Solid Hemisphere, Hollow Hemisphere and Frustum of a cone

19. Case study: Frustum of a cone

Exercise condition:

5 m.

Dhanush cuts the middle height of a metallic right circular cone of height 14 \(cm\) and whose vertical angle \(60^\circ\) into two parts by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter \(\frac{1}{10}\) \(cm\), find the following:

1. The radius of the lower side of the frustum:

$13 \sqrt{3} cm$
$\frac{14}{\sqrt{3}} cm$
$\frac{13}{\sqrt{3}} cm$
$14 \sqrt{3} cm$

2. The radius of the upper side of the frustum:

$5 \sqrt{3} cm$
$7 \sqrt{3} cm$
$\frac{5}{\sqrt{3}} cm$
$\frac{7}{\sqrt{3}} cm$

3. The volume of the wire:

$\frac{1647 π}{9} {cm}^{3}$
$\frac{1647 π}{3} {cm}^{3}$
$\frac{3254 π}{9} {cm}^{3}$
$\frac{2401 π}{9} {cm}^{3}$

4. The length of the wire:

\(4465.4 \ cm\)
\(5922.4 \ cm\)
\(1333.9 \ cm\)
\(6669.4 \ cm\)

5. Curved surface area of a frustum of a cone:

\(\pi (R - r) h\)
\(\pi (R + r) h\)
\(\pi (R + r) l\)
\(\pi (R - r) l\)

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