Question

A cone of height 8m has a curved surface arean188.4 sq metre if pie =3.14, find the radius of its base

Answer 1

ANSWER:-

Given:

A cone of height 8m has a curved surface area an 188.4 if π=3.14.

To find:

The radius of its base.

Explanation:

Let the radius of its base be r m

We know that formula of the curved surface area: πrl

&

We know that formula of the slant height: l= √(r²+h²)

A/q

⇒ πrl= 188.4m²

⇒ 3.14×r×√(r²+8²)= 188.4

⇒ 3.14×r×√(r²+64)= 188.4

⇒ r×√(r²+64)= $\frac{188.4*100}{3.14*100}$

⇒ r×√(r²+64)=$\frac{18840}{314}$

⇒ r×√(r²+64)=60

[ squaring both sides ]

⇒ [r√(r² +64)]²=[60]²

⇒ r²(r²+64)=3600

⇒ r^{4} +64r²= 3600

[ Factorise ]

⇒ r^{4} +64r² -3600=0

⇒ r^{4} +100r²-36r² -3600=0

⇒ r²(r²+100)-36(r²+100)=0

⇒ (r²+100)(r²-36)=0

⇒ r² +100=0   or   r²-36=0

⇒ r²= -100     or    r²=36

r²= -100 is negative value is not acceptable.

Therefore,

⇒ r² =36

⇒ r= √36

⇒ r= 6m.

Thus,

The radius of its base is 6m.

Answer 2

Given :-----

• CSA of cone = 188.4m²
• Height of cone = 8m
• pie = 3.14
• radius = ?

Formula used :-----

• CSA of cone = πrl
• l(slant height of cone) = √r²+h²

Putting above values in formula we get,

$3.14 \times r \times \sqrt{ {r}^{2} + {8}^{2} } = 188.4 \\ \\ r \times \sqrt{ {r}^{2} + 64} = \frac{188.4}{3.14} = 60 \\ \\ squaring \: both \: sides \: we \: get \\ \\ {r}^{2} (r^{2} + 64) = 3600 \\ \\ {r}^{4} + 64 {r}^{2} - 3600 = 0 \\ \\ let \: {r}^{2} = x \\ \\ {x}^{2} + 64x - 3600 = 0 \\ \\ {x}^{2} + 100x - 36x - 3600 = 0 \\ \\ x(x + 100) - 36(x + 100) = 0 \\ \\ (x + 100)(x - 36) = 0 \\ \\ x = - 100 \: or \: 36 \\ \\ {r}^{2} = 36 \\ \\ r = 6$

Hence , radius of cone is 6cm (Ans)

(Hope it helps you)