Step-by-step explanation:

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Answer:

[tex]\boxed{ \sf{ \: \sf \: Total \: quantity\:of\:canvas\:required \: = \: 15197.60 \: {m}^{2} \: }}\\ \\ [/tex]

Step-by-step explanation:

Given that, a circus tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 60 m and the height of the cylinder is 30 m. If the diameter of the base is 80 m.

So,

Dimensions of cylindrical portion

Height of cylinder, h = 30 m

Diameter of cylinder = 80 m

So, Radius of cylinder, r = 40 m

Now,

Dimensions of conical portion

Height of cone, H = 30 m

Radius of cone, r = 40 m

So, slant height (l) of cone is

[tex]\sf \: {l}^{2} = {r}^{2} + {h}^{2} \\ \\ [/tex]

[tex]\sf \: {l}^{2} = {40}^{2} + {30}^{2} \\ \\ [/tex]

[tex]\sf \: {l}^{2} = 1600 + 900 \\ \\ [/tex]

[tex]\sf \: {l}^{2} = 2500 \\ \\ [/tex]

[tex]\sf\implies \sf \: l = 50 \: m \\ \\ [/tex]

Now,

[tex]\sf \: Quantity\:of\:canvas\:required \\ \\ [/tex]

[tex]\sf \: = \: CSA \: of \: cylinder \: + \: CSA \: of \: cone \\ \\ [/tex]

[tex]\sf \: = \: 2\pi \: r \: h \: + \: \pi \: r \: l \\ \\ [/tex]

[tex]\sf \: = \: \pi \: r \:(2 h \: + \: l )\\ \\ [/tex]

[tex]\sf \: = \: 3.14 \times 40 \times (2 \times 30 + 50) \\ \\ [/tex]

[tex]\sf \: = \: 125.6 \times (60 + 50) \\ \\ [/tex]

[tex]\sf \: = \: 125.6 \times 110 \\ \\ [/tex]

[tex]\sf \: = \: 13816 \: {m}^{2} \\ \\ [/tex]

As it is given that, the quantity of canvas required to make the tent allowing 10% extra for stitching.

So,

[tex]\sf \: Total \: quantity\:of\:canvas\:required \\ \\ [/tex]

[tex]\sf \: = \: 13816 + 10\% \: of \: 13816 \\ \\ [/tex]

[tex]\sf \: = \: 13816 + \dfrac{10}{100} \: \times \: 13816 \\ \\ [/tex]

[tex]\sf \: = \: 13816 + \dfrac{1}{10} \: \times \: 13816 \\ \\ [/tex]

[tex]\sf \: = \: 13816 +1381.6 \\ \\ [/tex]

[tex]\sf \: = \: 15197.60 \: {m}^{2} \\ \\ [/tex]

Hence,

[tex]\sf\implies \sf \: Total \: quantity\:of\:canvas\:required \: = \: 15197.60 \: {m}^{2} \\ \\ [/tex]