Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.
(a)15 cm
(b)20 cm
(c)25 cm
(d)30 cm
Answer
Answer (as printed): A
Explanation
Volume of bucket $=28.490$ litres $=(28.490 \times 1000) \mathrm{cm}^{3}=28490 \mathrm{cm}^{3}$. Let the height of the bucket be $h$ cm. We have : $r=21 \mathrm{cm}, R=28 \mathrm{cm}$. $$\begin{aligned} & \therefore \frac{\pi}{3} h\left[(28)^{2}+(21)^{2}+28 \times 21\right]=28490 \\ & \Rightarrow h(784+441+588)=\frac{28490 \times 21}{22} \\ & \Rightarrow 1813 h=27195 \Rightarrow h=\frac{27195}{1813}=15 \mathrm{cm} . \end{aligned}$$