Question

A bucket is in form of frustrum of a cone and holds 28.490 L
of water. The radii of the top and bottom are 14 cm and 21cm respectively. find the height of the bucket

Answer 1

$\Large{\underline{\underline{\bf{GIVEN:-}}}}$

• Volume of frustum = 28.490 L
• Top radius(r1) = 14 cm
• Bottom radius(r2) = 21 cm

$\Large{\underline{\underline{\bf{TO \: FIND:-}}}}$

• What is the height of the bucket ?

$\Large{\underline{\underline{\bf{SOLUTION:-}}}}$

Let the height of the bucket be 'h' cm

We know that the formula for finding the volume of Frustum is:-

$\large{\boxed{\bf{\star \: V = \dfrac{1}{3} \pi h [ {r_1}^{2} + {r_2}^{2} + r_1 r_2 ] \: \star}}}$

According to question:-

On putting the values in the formula, we get

Take π = 22/7

$\sf{\longrightarrow 28.490 = \dfrac{1}{3} \times \dfrac{22}{7} \times h [(14)^2 + (21)^2 + 14 \times 21 ] }$

$\sf{\longrightarrow 28.490 \times 3 = \dfrac{22}{7} \times h [196 + 441 + 294 ] }$

$\sf{\longrightarrow 85.47 = \dfrac{22}{7} \times h \times 931}$

$\longrightarrow$ 85.47 = 22 $\times$ h $\times$ 133

$\sf{ \longrightarrow \cancel\dfrac{85.47}{2926} = h}$

⠀⠀❛ 0.029 m = h ❜

❝ Hence, the height of the frustum is 0.029 m ❞

______________________

Answer 2

$\huge \underline{ \blue{ \boxed{ \bf \orange{Answer:-}}}}$

• R = 28 cm
• r = 21 cm

Let height of frustum be h cm

∴ Volume held by bucket = 28.490 litres

= 28490 cm³

Also,

Volume of frustum = π(R²+Rr+r²)h/3

=> 28490 = 22*(784+588+441)*h/(3*7)

=> 1813h = 28490*21/22

=> h = 27195/1813 = 15cm

$\bf\blue{Hope\ it\ helps.}$

$\bf\pink{Plz\ Mark\ As\ Brainliest.}$