Question

the slant height and curved surface area of one cone is twice that of the Other can find the ratio of their radius​

Answer 1

Answer:

• The ratio of their radius = 1 : 1

Step-by-step explanation:

Let us assume:

• Curved surface area of one cone be A.
• Slant height of one cone be L.
• Radius of one cone be R.

• Curved surface area of other cone be a.
• Slant height of other cone be l.
• Radius of other cone be r.

Given that:

• The slant height and curved surface area of one cone is twice of the other.

Here,

⇒ A = 2a

⇒ L = 2l

To Find:

• The ratio of their radius.
• i.e., R : r

Formula used:

• Curved surface area of a cone = πrl

Where,

• Radius is denoted as r.
• Slant height is denoted as l.

Finding the ratio of their radius:

• According to the question.

⇒ πRL = 2πrl

• π cancelled both sides.

⇒ RL = 2rl [Given: L = 2l]

⇒ R × 2l = 2rl

⇒ R × 2l = r × 2l

• 2l cancelled both sides.

⇒ R = r

⇒ R/r = 1/1

⇒ R : r = 1 : 1

Answer 2

$\Large{\bf{Given\::}}$

• The slant height and Curved Surface Area of a cone is twice that of the other.

$\\ \Large{\bf{To\: Find\::}}$

• The ratio of their radius.

$\\ \Large{\bf{Solution\::}}$

Let,

☛ L₁ & L₂ be the slant height of (cone)₁ & (cone)₂ respectively.

☛ (C.S.A)₁ & (C.S.A)₂ be the curved surface area of (cone)₁ and (cone)₂ respectively.

And,

☛ r₁ & r₂ be the radius of (cone)₁ and (cone)₂ respectively.

According to the question,

⑴ L₁ = 2L₂

⑵ (C.S.A)₁ = 2 × (C.S.A)₂

As we know that,

✯ Curved Surface Area of cone is given as,

$\orange\bigstar\:\mid\:\bf\pink{C.S.A_{(cone)}\:=\:\pi\:r\:l\:}\:\mid\:\green\bigstar$

Now,

✯ We assume equation ⑵,

➳ (C.S.A)₁ = 2 × (C.S.A)₂

➳ π r₁ L₁ = 2 × (π r₂ L₂)

➳ π r₁ L₁ = 2πr₂L₂

➳ r₁ L₁ = 2 r₂ L₂

➳ r₁ (2L₂) = r₂ (2L₂) ⠀⠀[From equation 1]

➳ $\tt{\dfrac{r_1}{r_2}\:=\:\dfrac{2L_2}{2L_2}\:}$

➳ $\bf\pink{\dfrac{r_1}{r_2}\:=\:\dfrac{1}{1}\:}$

∴ The ratio of their radius is 1 : 1.