Question

Hi friends,

In a right circular cone, the height is 3 times the radius of the base. If it's volume is 134.75cm^3, find
(A) the area of the base
(B) the curved surface area.


Ans.
(A) 38.5 cm^2
(B) 108.88cm^2

Answer 1

$\textbf{Your answer is --}$

Let, height of circular cone be h and radius of circular cone r.

Since, the height is 3 times the radius of the base

So,

$\textbf{h = 3r ....(1)}$

Given, volume of circular cone is 134.75cm^3

Thus , 1/3πr^2h = 134.75

=> r^2h = (134.75×3×7)/22

=> r^2h = 128.625

=> h^3/9 = 128.625 [ from 1 ]

=> h^3 = 1157.625

=>$\textbf{10.5cm}$( since, cube root of 1157.625 is 10.5 )

put h = 10.5 in equation (1), we get

h = 3r.

=> r = 10.5/3

=> $\textbf{r ={3.5cm}$

$\textbf{(A)}$ Area of base = πr^2

= 22/7×3.5×3.5

$\textbf{= 38.5cm^2}$

$\textbf{(C)}$ $\textbf{Curved surface area is }$

l = √h^2+r^2

=> l = √110.25+12.25

=> l = √122.5

=> l = 11.05cm

$\textbf{Curved surface area }$ = πrl

= 22/7 × 3.5 × 11.05

= $\textbf{121.5cm^2}$

$\textbf{【 Hope it helps you 】}$

Answer 2

Step-by-step explanation:

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