Question

The radii of two cylinder ends of a frustum shaped bucket are 15 cm and 8 cm if its depth is 63 cm find the capacity of the bucket in litres?

Answer 1

Hey there!

Given radii of two circular ends of a frustum shaped bucket are 15 , 8cm .

We know that,

Volume of frustum of come = 1/3πh(R² + r² + rh)

So,
V = 1/3πh ( 15² + 8² + 15 * 8 )

= 1/3πh ( 225 + 64 + 120 )

= 1/3πh ( 289 + 120 )

= 1/3(22/7)(63)( 409 )

= 1/3 ( 22) ( 9 ) ( 409 )

= 22 * 3 * 409

= 26994 cm³

We know that,

1000cm³ = 1 litre


So, 26.994 * 1000 cm³ = 26.994 litres.

The capacity of the bucket is 26.994 litres.

Answer 2

$\bold{\large{\underline{Solution\: \colon}}}$

$\bold{\large{\underline{Given\: \colon}}}$

$\bold{\large{r_1 = 15 \: cm}}$

$\bold{\large{r_2 = 8 \: cm}}$

Depth of frustum = Height of frustum

$\bold{\large{h \: = \: 63\: cm}}$

$\bold{\large{\underline{To \: Find\: \colon}}}$

Capacity of frustum or bucket = volume of bucket

$\bold{\large{\underline{Solution\: \colon}}}$

We know the $\bold{capacity}$ of bucket is $\bold{volume}$ of frustum.

Volume of frustum  = $\bold{\large{\dfrac{1}{3}\pi\:h[(r_{1})^{2} +(r_{2})^{2} + r_1 . r_2]}}$

Put the values

$\bold{\large{\implies \dfrac{1}{3}\pi\:.\:63[(15)^{2} +(8)^{2} + 15\:.\:8]}}$

$\bold{\large{\implies 21\times\dfrac{22}{7}\times( 225 + 64 + 120)}}$

$\bold{\large{\implies 3\times22\times(409)}}$

$\bold{\large{\implies 26,994 \: cm^{3} }}$

In litres 1 cm³ = $\bold{0.001\: litres}$

Capacity of bucket in litres

$\bold{\large{ capacity \: in \: litres\: = \: 0.001\times 26994}}$

$\bold{\large{ \implies 26.994 \: litres}}$

$\bold{\underline{\large{Answer}}}$

$\bold{\large{ capacity \: of \: bucket \: is \: 27 \: litres}}$

$\bold{\large{Thanks}}$