question_answer

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many litres can the bucket hold?

A)  \[13\,L\]                     

B)  \[27\text{ }L\]            

C)  \[42.94\text{ }L\]      

D)         \[28.49\text{ }L\]                               

Correct Answer: D

Solution :

Volume of bucket           \[=\frac{\pi h}{3}[r_{1}^{2}+{{r}_{2}}^{2}+{{r}_{1}}{{r}_{2}}]\]             \[=\pi \times \frac{15}{3}[{{(28)}^{2}}+{{(21)}^{2}}+28+21]\] \[=28490\,c{{m}^{3}}\] \[\therefore \] Volume of bucket \[=28490\text{ }c{{m}^{3}}=28.49\]