Question

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 curved surface

Answer 1

Given :

• The radius and height of a cone are in the ratio 4:3.
• The area of the base is 154 cm².

To find :

• Curved surface area of the cone.

Solution :

Consider,

• Radius of cone = 4x cm
• Height of cone = 3x cm

Formula used :-

${\boxed{\sf{Area\:of\:base=\pi\:r^2}}}$

According to the question :-

$\to\sf{\pi\:r^2=154}$

$\to\sf{\dfrac{22}{7}\times\:(4x)^2=154}$

$\to\sf{\dfrac{22}{7}\times\:16x^2=154}$

$\to\sf{22\times\:16x^2=154\times\:7}$

$\to\sf{x^2=\dfrac{154\times\:7}{22\times\:16}}$

$\to\sf{x^2=\dfrac{49}{16}}$

$\to\sf{x=\sqrt{\dfrac{49}{16}}}$

$\to\sf{x=\dfrac{7}{4}}$

• Radius = $\sf{4\times\dfrac{7}{4}=7\:cm}$
• Height = $\sf{3\times\dfrac{7}{4}=5.25\:cm}$

Now find slant height (l) of the cone by using "Pythagoras Theorem" .

l² = h² + r²

→ l² = (5.25)² + 7²

→ l² = 27.56 + 49

→ l² = 76.56

→ l = 8.75

• Slant height = 8.75 cm

Formula Used :-

${\boxed{\sf{CSA\:of\: cone=\pi\:r\:l}}}$

Curved surface area,

= πrl

=( 3.14 × 7 × 8.75 ) cm²

= 192.33 cm² ( approx)

Therefore, the curved surface area of cone is 192.33 cm² (approx).

Answer 2

We have given the ratio of radius and height i.e 4 : 3

Let  

Radius = 4x

Height = 3x

Slant Height = root [(4x)2 +(3x)2 ]=5x {Pythagoras Theorem}

We know that  

Area of Base = pie X radius2  

154=22/7 X 16x2

--->x=1.75cm

Radius=7

Height =5.25cm

Slant Height =8.75cm  

Curved Surface Area = pie X radius x slant height

=22/7 X 7 X 8.75

-->x=192.5cm2