Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36m and 44 dm surmounted
by a right circular cone. Find the cost of the canvas at Rs.3.50 per m2
?

Answer 1

Answer:

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Step-by-step explanation:

The cost of the canvas at Rs.350m².

Solution:

⚫Height of tent= 77dm

In metre= 7.7m

⚫Diameter of the cylinder=36m

In radius = 36/2

=) 18m

⚫Height of cylinder= 44dm

In metre= 4.4m

⚫Height of cone= (7.7 -4.4)m

=) 3.3m

Curved surface area of cylinder portion of the tent;

=) 2πrh

\begin{gathered}= > 2 \times ( \frac{22}{7} ) \times 18 \times 4.4 \\ \\ = > \frac{44}{7} \times 79.2 \\ \\ = > \frac{3484.8}{7} \\ \\ = >497.82 {m}^{2}\end{gathered}

=>2×(

7

22

)×18×4.4

=>

7

44

×79.2

=>

7

3484.8

=>497.82m

2

Curved surface area of conical tent=πrl

Slant Height of cone:

\begin{gathered}= > \sqrt{(3.3) {}^{2} + 18 {}^{2} } \\ \\ = > \sqrt{10.89 + 324} \\ \\ = > \sqrt{334.89} \\ \\ = > 18.3m\end{gathered}

=>

(3.3)

2

+18

2

=>

10.89+324

=>

334.89

=>18.3m

Curved surface area of cone:

\begin{gathered}= > \frac{22}{7} \times 18 \times 18.3 \\ \\ = > \frac{7246.8}{7} \\ \\ = > 1035.26{m}^{2}\end{gathered}

=>

7

22

×18×18.3

=>

7

7246.8

=>1035.26m

2

Total Surface area of the tent:

=) 497.83m² + 1035.26m²

=) 1533.09m²

Total cost of canvas:

=) Rs.3.50 × 1533.09

=) Rs.5365.82

The cost of canvas is Rs.5365.82.

Hope it helps ☺️

Answer 2

Answer :

➥ The cost of canvas = Rs. 5365.82

Given :

➤ Height of the tent (h) = 77 dm

➤ Diameter of the cylinder (d) = 36 dm

➤ Height of cylinder (h) = 44 dm

To Find :

➤ The cost of canvas at ₹3.50 per m² = ?

Solution :

◈ Height of the tent = 77 dm = 7.7 m

◈ Radius of the cylinder = 36/2 = 8

◈ Height of the cylinder = 44 dm = 4.4 m

Height of the cone = 7.7 - 4.4

Height of the cone = 3.3 m

Curved surface area of the cylinder = 2πrl

$\tt{: \implies C.S.A = 2 \times \dfrac{22}{7} \times 18 \times 4.4}$

$\tt{: \implies C.S.A = \dfrac{44}{7} \times 18 \times 4.4 }$

$\tt{: \implies C.S.A = \dfrac{44}{7} \times 79.2}$

$\tt{: \implies C.S.A = \cancel{\dfrac{3784.8}{7} }}$

$\tt{: \implies \purple{ \underline{ \overline{ \boxed{ \green{ \bf{ \: \: C.S.A = 497.82 \: \: }}}}}}}$

Curved surface area of cone = πrl

Slant height of cone

$\tt{:\implies \sqrt{ {r}^{2} + {h}^{2} } }$

$\tt{: \implies \sqrt{ {(18)}^{2} + {(3.3)}^{2} } }$

$\tt{: \implies \sqrt{324 + 10.89} }$

$\tt{: \implies \sqrt{334.89} }$

$\bf{: \implies 18.3 \: m}$

Curved surface area of cone = πrl

$\tt{: \implies C.S.A = \dfrac{22}{7} \times 18 \times 18.3}$

$\tt{: \implies C.S.A = \cancel{\dfrac{7246.8}{7}} }$

$\tt{: \implies \purple{ \underline{ \overline{ \boxed{ \green{ \bf{ \: \: C.S.A = 1035.76\: \: }}}}}}}$

Now ,

Total surface area = Curved surface area of cylinder + Curved surface area of cone

$\tt{: \implies T.S.A = 497.83 + 1035.76}$

$\tt{: \implies \purple{ \underline{ \overline{ \boxed{ \green{ \bf{ \: \: T.S.A =1533.09 \: {m}^{2} \: \: }}}}}}}$

The cost of the canvas at Rs.3.50 per m²

$\tt{: \implies 1533.09 \times 3.50}$

$\tt{: \implies \green{ \underline{ \overline{ \boxed{ \purple{ \bf{ \: \: Rs. \: 5365.82\: \: }}}}}}}$

Hence, the cost of the canvas at Rs.3.50 per m² is Rs. 5365.82.