Question

39. A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm". The radii of the top and bottom of circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use π = 3.14)​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\huge\underline{ \underline{ \red{solve = > }}} \\ {{ \blue{the \: valume \: \: of \: bucket = 12308.8 {cm}^{3} }}} \: \\ {{ \blue{ r_{1} = 20cm \: }}} \: \\ {{ \blue{ r_{2} = 12cm }}} \: \\ {{ \blue{h = ?}}} \: \\ we \: have \: \\ valume \:of \: bucket = \frac{\pi h}{3}( { r_{1} }^{2} + { r_{2} }^{2} +r_{1}r_{2} )\\ 12308.8 = 3.14 \times \frac{h}{3} ( {20}^{2} + {12}^{2} + 20 + 12) \\ = > h = 12308.8 \times \frac{3}{3.14 \times 784} \\ h = 15 cm \\ height \: of \: the \: bucket \: (h) = 15cm \\ {{ \blue{surface \: area \: of \: the \: metal \: sheet \: used}}} \\ = \pi {r}^{2} + \pi(r_{1} + r_{2})l \\ l = \sqrt{ {h}^{2} } +( {r_{1} - r_{2}})^{2} \\ l = \sqrt{15 + {8}^{2} } = \sqrt{225 + 64} = 17cm \\ {{ \blue{surface \: area \: of \: the \: metal \: sheet \: used}}} \: \\ \pi {r_{2}}^{2} + \pi( r_{1} + r_{2})l \\ = > 3.14 \times {12}^{2} + \frac{22}{7} \times 32 \times 17 \\ 3.14(144 + 544) \\ = > 2160.32 {cm}^{2} \\ {{ \blue{hence = > }}} \\ height \: of \: the \: bucket = {{ \blue{15cm }}} \\ area \: of \: metal \: sheet \: used = {{ \blue{2160.32 {cm}^{2} }}}$