Question

A tent is in the shape of a right circular cylinder
upto a height of 3 m and conical above it. The total
height of the tent is 13.5 m above the ground.
Calculate the cost of painting the inner side of the
tent at the rate of 2 per m’, if the radius of the base
is 14 m. (jisko aata h whi answer kre nhi aata h th chup betha answer glt hua na tumko pitenga) ​

Answer 1

Given :

• Height of Cylinder = 3 m.
• Total Height of Tent = 13.5 m .
• Radius of the base = 14 m .

To Find :

• Cost of painting the inner side of the
• tent at the rate of 2 per m .

Solution :

Height of cone = 13.5-3 = 10.5 m .

Firstly we'll find the C.S.A of Cylinder :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{{\cancel{7}}}\times{{\cancel{14}}}\times{3}}$

$\longmapsto\tt{44\times{2}\times{3}}$

$\longmapsto\tt\bf{264\:{m}^{2}}$

Now , We'll calculate the Slant Height of Cone :

$\longmapsto\tt{{l}^{2}={(r)}^{2}+{(h)}^{2}}$

$\longmapsto\tt{{l}^{2}={(10.5)}^{2}+{(14)}^{2}}$

$\longmapsto\tt{{l}^{2}=110.25+196}$

$\longmapsto\tt{l=\sqrt{306.25}}$

$\longmapsto\tt\bf{l=17.5\:m}$

For C.S.A of Cone :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{\dfrac{22}{{\cancel{7}}}\times{{\cancel{14}}}\times{17.5}}$

$\longmapsto\tt{44\times{17.5}}$

$\longmapsto\tt\bf{770\:{m}^{2}}$

Total Area of Tent :

$\longmapsto\tt{264+770}$

$\longmapsto\tt\bf{1034\:{m}^{2}}$

Cost of painting it at the rate of ₹ 2 per m :

$\longmapsto\tt{1034\times{2}}$

$\longmapsto\tt\bf{Rs.2068}$

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar\:{\underline{\pmb{\sf{\purple{Understanding \: the \: question:}}}}}}$

⋆ This question says that a tent is in the shape of a right circular cylinder upto a height of 3 m and conical above it. The total height of the tent is 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of 2 per m if the radius of the base is 14 metres. Let us solve this question!

${\bigstar\:{\underline{\pmb{\sf{\purple{Given \: that:}}}}}}$

⋆ A tent is in the shape of a right circular cylinder upto a height of 3 metres and conical above it.

⋆ The total height of the tent is 13.5 metres above the ground.

⋆ The radius of the base is 14 metres

${\bigstar\:{\underline{\pmb{\sf{\purple{To \: find:}}}}}}$

⋆ The tent at the rate of 2 per metres

${\bigstar\:{\underline{\pmb{\sf{\purple{Solution:}}}}}}$

⋆ The tent at the rate of 2 per metres = 2068 rs.

${\bigstar\:{\underline{\pmb{\sf{\purple{Using \: concepts:}}}}}}$

⋆ Formula to find out the curved surface area of the cylinder.

⋆ Formula to find out the curved surface area of the cone.

⋆ Formula to find out the slant height of the cone.

⋆ Formula to find total area of the tent

⋆ Formula to find the rate.

${\bigstar\:{\underline{\pmb{\sf{\purple{Using \: formulas:}}}}}}$

${\small{\underline{\boxed{\sf{\star \: CSA \: of \: cylinder \: = 2 \pi rh}}}}}$

${\small{\underline{\boxed{\sf{\star \: CSA \: of \: cone \: = \pi rl}}}}}$

${\small{\underline{\boxed{\sf{\star \: Slant \: height \: of \: cone \: = (l)^{2} \: = (r)^{2} + (h)^{2}}}}}}$

${\small{\underline{\boxed{\sf{\star \: Total \: area \: = CSA \: of \: cylinder \: + CSA \: of \: cone}}}}}$

${\small{\underline{\boxed{\sf{\star \: Rate \: = Given \: amount \times Total \: area}}}}}$

${\bigstar\:{\underline{\pmb{\sf{\purple{Full \: Solution:}}}}}}$

~ Firstly by using the formula of find CSA of cylinder let us find CSA!

${\small{\underline{\boxed{\sf{CSA \: of \: cylinder \: = 2 \pi rh}}}}} \\ \\ :\implies \sf CSA \: of \: cylinder \: = 2 \pi rh \\ \\ :\implies \sf CSA \: of \: cylinder \: = 2 \times 3.14 \times 14 \times 3 \\ \\ :\implies \sf CSA \: of \: cylinder \: = 6.27 \times 14 \times 3 \\ \\ :\implies \sf CSA \: of \: cylinder \: = 6.27 \times 42 \\ \\ :\implies \sf CSA \: of \: cylinder \: = 264 \: m^{2}$

Henceforth, CSA of cylinder = 264m²

~ Now by using the formula of find out the slant height of cone let us find length.

${\small{\underline{\boxed{\sf{Slant \: height \: of \: cone \: = (l)^{2} \: = (r)^{2} + (h)^{2}}}}}} \\ \\ :\implies \sf Slant \: height \: of \: cone \: = (l)^{2} \: = (r)^{2} + (h)^{2} \\ \\ :\implies \sf (l)^{2} \: = (r)^{2} + (h)^{2} \\ \\ :\implies \sf (l)^{2} \: = (10.5)^{2} + (14)^{2} \\ \\ :\implies \sf (l)^{2} \: = 110.25 + 196 \\ \\ :\implies \sf (l)^{2} \: = 306.25 \\ \\ :\implies \sf l \: = \sqrt{306.25} \\ \\ :\implies \sf l \: = 17.5 \: metres$

• *Note: Don't be confused that how height is came as 10.5 as it's 13.5 It came like as because one more height is given as 3. So, 13.5-3 = 10.5 metres.

Henceforth, length = 17.5 metres

~ Now by using the formula to find CSA of cone let's find CSA.

${\small{\underline{\boxed{\sf{CSA \: of \: cone \: = \pi rl}}}}} \\ \\ :\implies \sf CSA \: of \: cone \: = \pi rl \\ \\ :\implies \sf CSA \: of \: cone \: = 3.14 \times 14 \times 17.5 \\ \\ :\implies \sf 770 \: metres^{2}$

Henceforth, 770 m² = CSA here

~ Now let's find out the total area of tent.

${\small{\underline{\boxed{\sf{Total \: area \: = CSA \: of \: cylinder \: + CSA \: of \: cone}}}}} \\ \\ :\implies \sf Total \: area \: = CSA \: of \: cylinder \: + CSA \: of \: cone \\ \\ :\implies \sf Total \: area \: = 264 + 770 \\ \\ :\implies \sf Total \: area \: = 1034 \: m^{2}$

Henceforth, 1034 m² = Total area.

~ Now at last let us find the rate.

${\small{\underline{\boxed{\sf{Rate \: = Given \: amount \times Total \: area}}}}} \\ \\ :\implies \sf Rate \: = Given \: amount \times Total \: area \\ \\ :\implies \sf Rate \: = 2 \times 1034 \\ \\ :\implies \sf Rate \: = 2068 \: Rupees$

Therefore, rate is 2068 Rs.