Question

Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100π m wide.

Answer 1

The length of cloth used in making a conical pandal is 624 meter

Solution:

Given that,

Height of conical pandal = 100m

Base radius of pandal = 240 m

Find the slant height

$l = \sqrt{r^2+h^2}\\\\l = \sqrt{240^2 + 100^2 }\\\\l = \sqrt{67600}\\\\l = 260\ meter$

Find the curved surface area of cloth

$CSA = \pi rl\\\\CSA = \pi \times 240 \times 260$

Given that,

cloth is 100π m wide

Therefore,

$\text{length of 100 } \pi \text{ meter wide cloth } = \frac{\text{ curved surface area of cloth}}{ \text{ width of cloth }}$

$\text{length of 100 } \pi \text{ meter wide cloth } = \frac{ \pi \times 240 \times 260 }{100 \times \pi }\\\\\text{length of 100 } \pi \text{ meter wide cloth } = 24 \times 26\\\\\text{length of 100 } \pi \text{ meter wide cloth } =624$

Thus the length of cloth used in making a conical pandal is 624 meter

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