Question

the radius and the slant height of a cone are in the ratio of 4:7. if the curved area is 792 cm square then find the radius

Answer 1

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C.S.A of a cone

$= \pi r l$

$22/7 * 4x * 7x = 792$

$22/7 * 28x^2 = 792$

$22*4x^2= 792$

$4x^2 = 792/22$

$4x^2 = 36$

$x^2 = 36/4$

$x = \sqrt {36/4}$

$x = 6/2$

$x = 3$

Radius will be

$= 4x$

$= 4*3$

$= 12 cm$

Answer 2

Step-by-step explanation:

Given

The radius and slant of height of a cone are in the ratio 4:7

Curved Surface Area is 792 cm²

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To Find

The radius

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Solution

Let's consider the radius to be '4x' and height be '7x' (Here we have taken the radius as 4x and 7x since they are in the ratio of 4:7)

Formula to find the curved surface area of a cone ⇒ πrl

Here,

'r' stands for radius.

'l' stands for the slant height.

Curved surface area of the cone ⇒ 729 cm²

Let's solve the equation step-by-step

22/7×4x×7x =792

Step 1: Simplify the equation.

⇒ 22/7 4x × 7x = 729

⇒22/7×28x² =729

=22×4x²= 792

=88x²=792

Step 2: Divide 88 from both sides of the equation.

⇒ 88x²/88 = 792/88

Step 3: Find the square root of 9.

⇒ x=√9

= x=3

∴ The radius ⇒ 4x ⇒ 4(3) ⇒ 12 cm

∴ The slant height of cone ⇒ 7x ⇒ 7(3) ⇒ 21 cm

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