Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

The radius and height of a cone are in the ratio 4:3 . The area of the base is 154 cm^2 . Find the area of the curved surface .

Answers (1)

best_answer

Solution: Let $r$ be the radius and $h$ be the height of the cone . it is given that

$fracrh= frac43$

Let $r= 4x$ and $h= 3x$

Now , Area of the base $= 154$ $cm^2$

$Rightarrow$ $pi r^2=154$

$Rightarrow$ $frac227 imes (4x)^2=154$

$Rightarrow$ $frac227 imes 16 x^2=154$

$Rightarrow$ $x^2= frac154 imes 722 imes 16=frac4916Rightarrow x= sqrtfrac4916=frac74cm$

$herefore$ $r=4x=4 imes frac74cm ,$ and $h= 3 imes frac74=frac214cm$

Let the slant height be $l$ cm . Then,

$l^2=r^2+h^2$

$Rightarrow$ $l=sqrtr^2+h^2=sqrt7^2+ (frac214)^2cm = sqrt49+frac44116=frac354cm$

$herefore$ curved surface area

$=pi rl = frac227 imes7 imes frac354cm^2=192.5cm^2$

Posted by

Deependra Verma

View full answer

Similar Questions

Latest Question