A metallic cone with radius 5 , cm and height | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The volume of the metallic cone is given by the formula $V_{cone} = \frac{1}{3} \pi r^2 h$. Substituting the given values $r = 5 \, cm$ and $h = 8

Vedclass · Accepted Answer

$3200$

Vedclass · Answer

(C) The volume of the metallic cone is given by the formula $V_{cone} = \frac{1}{3} \pi r^2 h$. Substituting the given values $r = 5 \, cm$ and $h = 8 \, cm$,we get $V_{cone} = \frac{1}{3} \pi (5)^2 (8) = \frac{200}{3} \pi \, cm^3$.The volume of each spherical ball with diameter $0.5 \, cm$ (radius $r_b = 0.25 \, cm = \frac{1}{4} \, cm$) is $V_{ball} = \frac{4}{3} \pi r_b^3 = \frac{4}{3} \pi (\frac{1}{4})^3 = \frac{4}{3} \pi (\frac{1}{64}) = \frac{1}{48} \pi \, cm^3$.The number of balls produced is $n = \frac{V_{cone}}{V_{ball}} = \frac{\frac{200}{3} \pi}{\frac{1}{48} \pi} = \frac{200}{3} 	imes 48 = 200 	imes 16 = 3200$.

$A$ metallic cone with radius $5 \, cm$ and height $8 \, cm$ is melted and recast to produce identical balls with diameter $0.5 \, cm$. Find the number of balls produced.

Similar Questions

The $TSA$ (Total Surface Area) of a $5$-rupee coin is given by the formula $\ldots \ldots \ldots . .$

Two cones with the same base radius $8\, cm$ and height $15\, cm$ are joined together along their bases. Find the surface area of the shape so formed. (in $cm^2$)

$A$ heap of rice is in the form of a cone of diameter $9 \, m$ and height $3.5 \, m$. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Three metallic solid cubes whose edges are $3 \, cm$,$4 \, cm$,and $5 \, cm$ are melted and formed into a single cube. Find the edge of the cube so formed (in $cm$).

Two solid cones $A$ and $B$ are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is $2:1$. Find the heights and capacities of the cones. Also,find the volume of the remaining portion of the cylinder (in $cm^{3}$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module