Question

cone
The diameter and slant height of a
1 are in the ratio 8:7 find its
slant height & If
its curved rurface are
is 3186 m²
​

Answer 1

Correct Question:

The diameter and slant height of a cone are in the ratio 8:7. If its curved surface area is 3186 m². Then find its slant height.

Given:

✰ The diameter and slant height of a cone are in the ratio 8:7.

✰ Curved surface area of a cone = 3186 m²

To find:

✠ The slant height of a cone.

Solution:

Let's understand the concept first! First we will assume the diameter and the slant height of a cone as 8x and 7x respectively. Diameter is nothing but half the radius. Like this will find the radius of a cone. We are provided with the curved surface area of a cone. After that we will substitute its value in the formula of curved surface area to find the value of x. Then we will substitute the value of x in the slant height to find the slant height of a cone.

Let the diameter of a cone be 8x and the slant height of a cone be 7x.

⤳ Radius = Diameter/2

⤳ Radius = 8x/2

✭ Curved surface area = πrl ✭

Where,

• r is the radius of a cone.
• l is the slant height of a cone.

Putting the values in the formula, we have:

➤ 3186 = 22/7 × 8x/2 × 7x

➤ 3186 = 11/7 × 8x × 7x

➤ 3186 = 11 × 8x × x

➤ 3186 = 88x²

➤ x² = 3186/88

➤ x² = 36.205

➤ x = √36.205

➤ x = 6.017

Now, find the slant height of a cone by substituting the value of x

➛ Slant height of a cone = 7 × 6.017

➛ Slant height of a cone = 42.119 cm

∴ The slant height of a cone = 42.119 cm

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