Name: Conversion of Solids
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: What happens when a goldsmith heats a gold bar to create something? The gold bar's shape gets changed. But what about its volume? Does it change too? Find ou...

Question

A right triangle, whose sides are

3 c m

and

4 c m

( other than hypotenuse ) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. ( Choose value of

π

as found appropriate )

Accepted Answer

Double cone so formed by revolving this right angle triangle $A B C$ about its hypotenuse is shown in figure.

Hypotenuse $A C = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 c m$

Area of $∆ ABC = \frac{1}{2} \times OB \times AC = \frac{1}{2} \times AB \times BC$

$\Rightarrow \frac{1}{2} \times A C \times O B = \frac{1}{2} \times 4 \times 3$

$\Rightarrow \frac{1}{2} \times 5 \times O B = \frac{12}{2}$

$\Rightarrow O B = \frac{12}{5} = 2 .4 cm$

Volume of double cone $=$ volume of cone $1 +$ volume of cone $2$

$= \frac{1}{3} π r^{2} h_{1} + \frac{1}{3} π r^{2} h_{2}$

$= \frac{1}{3} π r^{2} (h_{1} + h_{2}) = \frac{1}{3} π r^{2} (O A + O C)$

$= \frac{1}{3} \times \frac{22}{7} \times {(2.4)}^{2} (5)$

$= 30 .14 c m^{3}$

Surface area of double cone $=$ surface area cone $1 +$ surface area of cone $2$

$= π r l_{1} + π r l_{2}$

$= π r [4 + 3] = \frac{22}{7} \times 2.4 \times 7$

$= 52 .8 {cm}^{2}$

A right triangle, whose sides are $3 c m$ and $4 c m$ ( other than hypotenuse ) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. ( Choose value of $π$ as found appropriate )

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A right triangle, whose sides are 3 cm and 4 cm ( other than hypotenuse ) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. ( Choose value of π as found appropriate )

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A right triangle, whose sides are $3 c m$ and $4 c m$ ( other than hypotenuse ) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. ( Choose value of $π$ as found appropriate )