A 15 cm tall cylindrical bucket of base diameter 6 cm, is recast to form a frustum with radii 2 cm and 4 cm. Find the height of the frustum obtained.

11.75 cm

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14.47 cm

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13.21 cm

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12.52 cm

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Solution

The correct option is B
14.47 cm

Given, height of cylindrical bucket, h = 15 cm
diameter of the cylindrical bucket = 6 cm
So, radius of bucket, r = $\frac{6}{2}$ = 3 cm.

Volume of the cylinder
$= π r^{2} h$
$= π \times (3)^{2} \times 15 = 135 π c m^{3}$

Given, radii of frustum; r' = 2 cm and R = 4 cm.
Let h' be the height of the frustum.

Volume of the frustum
= $\frac{1}{3} π (R^{2} + (r^{'})^{2} + R \times r^{'}) h^{'}$
$= \frac{1}{3} π \times (4^{2} + 2^{2} + 4 \times 2) \times h^{'} = 9.33 π h^{'} c m^{3}$

Given, cylindrical bucket is recast into a form of frustum. So, the shape changes but volume remains the same.
Volume of cylinder = Volume of frustum
135 $π$ = 9.33 $π h^{'}$
$h^{'} = \frac{135}{9.33} c m$
$h^{'} = 14.47 c m$

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Similar questions

Q. The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.

Q. The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is

(a) 6 cm

(b) 8 cm

(c) 4 cm

(d) 7 cm

Q. A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 cm

The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 respectively. Find the slant height of the frustum.

Match the following columns:

$\begin{matrix} C o l u m n I & C o l u m n I I (a) T h e r a d i i o f c i r c u l a r e n d s o f & (p) 2418 π a b u c k e t i n t h e f o r m o f f r u s t u m o f a c o n e o f h e i g h t 30 c m a r e 20 c m a n d 10 c m r e s p e c t i v e l y . T h e c a p a c i t y o f t h e b u c k e t i s . . . . . c m^{3} . [T a k e π = \frac{22}{7} .] (b) T h e r a d i i o f t h e c i r c u l a r e n d s & (q) 22000 o f a c o n i c a l b u c k e t o f h e i g h t 15 c m a r e 20 c m a n d 12 c m r e s p e c t i v e l y . T h e s l a n t h e i g h t o f t h e b u c k e t i s . . . . c m . (c) T h e r a d i i o f t h e c i r c u l a r e n d s & (r) 12 o f a s o l i d f r u s t u m o f a c o n e a r e 33 c m a n d 27 c m a n d i t s s l a n t h e i g h t i s 10 c m . T h e t o t a l s u r f a c e a r e a o f t h e b u c k e t i s . . . . . c m^{2} . (d) T h r e e s o l i d m e t a l l i c s p h e r e s o f & (s) 17 r a d i i 3 c m, 4 c m a n d 5 c m a r e m e l t e d t o f o r m a s i n g l e s o l i d s p h e r e . T h e d i a m e t e r o f t h e r e s u l t i n g s p h e r e i s . . . . . . c m . \end{matrix}$

The correct answer is

$(a) -_{. . . . . . . .,}$ $(b) -_{. . . . . . . .,}$ $(c) -_{. . . . . . . .,}$ $(d) -_{. . . . . . . . .}$

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