Question

radius and slant height of a cone is in the form a ratio of 4:7. if curved surface area of cone is 792 cm² then find its radius. ​

Answer 1

Given :-

• Ratio of Radius and slant height = 4 : 7
• Curved Surface Area = C.S.A = 792 cm²

To find :-

• Radius of cone

Assumption :-

• Let Ratio be in x form as
• Radius = 4x
• Slant height = 7x

Formula used :-

• ${ \underline{ \boxed{ \sf{C.S.A = \pi rl}}}}$
• Here , π = pi = 22/7
• r = Radius
• l = Slant height

Solution :-

•Substituting the values in formula for finding value of x :-

${ \implies{ \sf{C.S.A = \pi rl}}}$

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

${ \implies{ \sf{792 = \cfrac{22}{7} \times 28x^2}}}$

${ \implies{ \sf{792 = 22 \times 4 {x}^{2} }}}$

${ \implies{ \sf{ \cfrac{792}{22} = 4 {x}^{2} }}}$

${ \implies{ \sf{ 36 = 4 {x}^{2} }}}$

${ \implies{ \sf{ \cfrac{36}{4} = {x}^{2} }}}$

${ \implies{ \sf{ {x}^{2} = 9}}}$

${ \implies{ \sf{ x = \sqrt{9} }}}$

${ \underline{ \boxed{ \blue{ \implies{ \sf{ x = 3 }}}}}}$

● So, Radius of the cone is :-

$\large{\longmapsto{ \sf{Radius = 4x }}} \\ \\ \large{\longmapsto{ \sf{Radius = 4(3) }}} \\ \\ \large{ \underline{ \boxed{ \red{\longmapsto{ \sf{Radius = 12 \: cm}}}}}}$

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VERIFICATION :-

• Before verification we need to find Slant height of the cone. So, slant height is :-

• Slant Height = 7x = 7(3) = 21 cm .

VERIFICATION:-

${ \implies{ \sf{C.S.A = \pi rl}}}$

${ \implies{ \sf{792 = \cfrac{22}{7} \times 12 \times 21}}}$

${ \implies{ \sf{792 = 22 \times 12 \times 3}}}$

${ \implies{ \sf{792 = 792}}}$

LHS = RHS

Here, LHS is equal to RHS , so our answers are correct.

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More to know :-

More formulas related to Cone :-

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$

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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