Question

A bucket is in the form of a frustum of a cone. Its depth is 15cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold. [Take π=22/7]

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Bucket\:can\:hold=28.4\:litre}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: {\implies Height \: of \: glass = 15\: cm} \\ \\ \tt: {\implies Diameter \: of \: glass ( d_{1})=56\: cm} \\ \\ \tt: {\implies Diameter \: of \: glass ( d_{2})=42\: cm} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Volume \: of \: Bucket = ?$

• According to given question :

$\tt \circ \: r_{1} = 28 \: cm \\ \\ \tt \circ \: r_{2} = 21 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: glass = \frac{1}{3} \pi h(( r_{1})^{2} + {( r_{2} )}^{2} + ( r_{1} \times r_{2})) \\ \\ \tt: \implies Volume \: of \: Bucket = \frac{1}{3} \times \frac{22}{7} \times 15\times ( {28}^{2} + {21}^{2} + (28 \times 21)) \\ \\ \tt: \implies Volume \: of \:Bucket = \frac{1}{3} \times \frac{22}{7} \times 15 \times (784 + 441+ 588) \\ \\ \tt: \implies Volume \: of \: Bucket= \frac{1}{3} \times \frac{22}{7} \times 15\times 1813 \\ \\ \green{\tt: \implies Volume \: of \: Bucket = 28490 \: {cm}^{3} }$

$\bold{As \: we \: know \: that} \\ \tt: \implies {1 \: cm}^{2} = \frac{1}{1000} \: litre \\ \\ \tt: \implies 28490 \: {cm}^{2} = \frac{1}{1000} \times 28490 \\ \\ \green{ \tt\therefore Bucket \: can \: hold \: 28.4 \: litre \: water}$