Practice | Hashtable

1. The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is :

A. 19404 dm³

B. 194.04 dm³

C. 19.404 dm³

D. 1940.4 dm³

Solution:

The volume of cone should be maximum
∴ Radius of the base of cone :

\begin{aligned} = \frac{Edge of cube}{2} \\ = \frac{4.2}{2} \\ = 2.1 dm. \end{aligned}

Height of cone = Edge of cube = 4.2 dm.
∴ Volume of cone :

\begin{aligned} = \frac{1}{3} π r^{2} h \\ = (\frac{1}{3} \times \frac{22}{7} \times 2.1 \times 2.1 \times 4.2) cu .dm . \\ = 19.404 cu .dm . \end{aligned}

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