question_answer

The radii of the ends of a bucket of height 24 cm are 15 cm and 5 cm. Then, its capacity is

A)  \[8000\,\,c{{m}^{3}}\]           

B)  \[8100\,\,c{{m}^{3}}\]

C)  \[8171.43\,\,c{{m}^{3}}\]       

D)  \[8200.43\,\,c{{m}^{3}}\]

Correct Answer: C

Solution :

Capacity of bucket = Volume of frustum of a cone \[=\frac{\pi h}{3}[{{R}^{2}}+{{r}^{2}}+\operatorname{Rr}]=\frac{22}{7}\times \frac{24}{3}[{{(15)}^{2}}+{{5}^{2}}+15\times 5]\,\,c{{m}^{2}}\]\[=\frac{22}{7}\times 8\,\,[225+25+75]\,\,c{{m}^{3}}=\frac{176}{7}(325)\,\,c{{m}^{3}}\] \[=817143.\,\,c{{m}^{3}}\]