Question

the c.s.a of cone is 4070c.m2 and its diameter is 70c.m.find it's slant height​

Answer 1

Answer:

• 37 cm

Given:

• Curved surface area of cone = 4070 cm².
• Diameter of cone = 70 cm
• Radius of cone = 35 cm

To find:

• Slant height of cone?

Solution:

☯ Let Slant height of cone be l cm.

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$\setlength{\unitlength}{1.6mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{35 cm}}\put(22,10){\sf{l cm}}\end{picture}$

⠀━━━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Curved\;Surface\;Area_{\;(cone)} = \pi rl}}}}$

Here,

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• CSA = 4070 cm²
• r = 35 cm

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$\dag\;{\underline{\frak{Putting\;values,}}}$

$:\implies\sf \dfrac{22}{ \cancel{7}} \times \cancel{35} \times l = 4070$

$:\implies\sf 22 \times 5 \times l = 4070$

$:\implies\sf 110 \times l = 4070$

$:\implies\sf l = \cancel{ \dfrac{4070}{110}}$

$:\implies{\underline{\boxed{\frak{\purple{l = 37\;cm}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Slant\;height\;of\;cone\;is\; {\textsf{\textbf{37\;cm}}}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\:More\:to\:know :}}}}}\mid}$

• Curved surface area of cone = πrl

• Total surface area of cone = πr(l + r)

• Volume of cone = ⅓πr²h

• Curved surface area of cylinder = 2πrh

• Total surface area of cylinder = 2πr(h + r)

• Volume of cylinder = πr²h

Answer 2

Question :

The CSA of cone is 4070 cm² and its diameter is 70 cm .Find it's slant height.

Answer :

$\sf Given \begin{cases} & \sf{CSA \: of \: the \: cone = \bf{4070 \: cm^{2}}} \\ & \sf{Diameter \: of \: cone = \bf{70 \: cm}} \end{cases}$

$\sf Find \begin{cases} & \sf{Slant \: height \: of \: the \: cone} \end{cases}$

$\sf Solution \begin{cases} & \sf{Slant \: height \: of \: cone = \bf{37 \: cm}} \end{cases}$

$\sf Using \; concept \begin{cases} & \sf{Curved \: surface \: area \: of \: cone} \end{cases}$

$\sf Using \; formula \begin{cases} & \sf{\pi rl} \end{cases}$

What does the question say ?

• This question says that we have to find the slant height of the given cone whose CSA is given as 4070 cm² and diameter is given as 70 cm.

We also write these as :

• pi as π.
• diameter as d.
• radius as r
• curved surface area as CSA
• Value of π is 22/7

Assumption :

• Slant height as l

Converting diameter into radius :

• Radius = Diameter / 2
• Radius = 70 / 2
• Radius = 35 cm.

How to solve this question :

• To solve this question as we already convert d into r so now using the formula to find CSA of the cone we have to put the values and we get our result very easily

Full solution :

Curved surface area of cone = πrl

[Putting the values]

$\implies$ 4070 = 22/7 × 35 × l

[Cancel 35 and 7 we get 5 because 7 × 5 = 35 always]

$\implies$ 4070 = 22 × 5 × l

[Multiplying 22 by 5 we get 110]

$\implies$ 4070 = 110 × l

$\implies$ 4070/110 = l

$\implies$ 407/110 = l

$\implies$ 37 = l

$\implies$ l = 37 cm

Hence, the slant height of the given cone is 37 cm.

More knowledge -

Diagram of the question to understand this question properly and easily.

$\setlength{\unitlength}{1.6mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{35 cm}}\put(22,10){\sf{l cm}}\end{picture}$

What is a cone ?

A cone is a three-dimensionap (3D) shape that smoothly from a flat base to a point called the vertex.

Some formulas related to cone are given below ↓

➨ Volume of cone = π × r² × (h/3)

➨ CSA of cone = πrl

➨ Base area of cone = πb²

Diagram of a cone to understand all the concepts easily.

See the above attachment (top)

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