Question

The radius and slant height of a cone are in the ratio 4:7. If it's curved surface area is 792 sq cm, find it's radius.
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Answer 1

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

$\sf \dfrac{22}{7} \times 4x \times 7x = 792$

Step 1: Simplify the equation.

⇒ $\sf \dfrac{22}{7} \times 4x \times 7x = 729$

⇒ $\sf \dfrac{22}{7} \times 28x^{2} = 792$

⇒ $\sf 22\times 4x^{2} =792$

⇒ $\sf 88x^{2} = 792$

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

⇒ $\sf \dfrac{88x^{2}}{88} = \dfrac{792}{88}$

⇒ $\sf x^{2} = 9$

Step 3: Find the square root of 9.

⇒ $\sf x = \sqrt{9}$

⇒ $\sf x = 3$

∴ The radius ⇒ 4x ⇒ 4(3) ⇒ 12 cm

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

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Answer 2

Given :-

• The radius and slant height of a cone are in the ratio of 4 : 7 and its curved surface area is 792 cm².

To Find :-

• What is the radius.

Formula Used :-

$\boxed{\bold{\large{C.S.A\: of\: cone\: =\: {\pi}rl}}}$

where,

• C.S.A = Curved Surface Area
• r = Radius
• l = Slant Height

Solution :-

Let, the radius be 4x

And, the slant height will be 7x

Given :

• Curved surface area = 792 cm²
• Radius = 4x
• Slant height = 7x

According to the question by using the formula we get,

⇒ $\sf \dfrac{22}{7} \times 4x \times 7x =\: 792$

⇒ $\sf \dfrac{22}{7} \times 28{x}^{2} =\: 792$

⇒ $\sf {r}^{2} =\: \dfrac{792 \times 7}{22 \times 28}$

⇒ $\sf {r}^{2} =\: \dfrac{5544}{616}$

⇒ $\sf {r}^{2} =\: \dfrac{\cancel{5544}}{\cancel{616}}$

⇒ $\sf {r}^{2} =\: 9$

⇒ $\sf r =\: \sqrt{9}$

➠ $\sf\bold{\red{r =\: 3\: cm}}$

Hence, the required radius and slant height are,

✧ Radius = 4x = 4(3) = 12 cm

✧ Slant height = 7(3) = 21 cm

$\therefore$ The radius of cone is 12 cm .