Question

A conical cup is made from a circular piece of paper with radius 6 cm by cutting out a sector and joining the edges as shown below. Suppose θ = 5π/3.

Answer 1

The
`r`,
`h`, and 6 cm form a right triangle, so you find
`h` with the Pythagorean Theorem.


`r^(2)+h^(2)=6^(2)`
We have
`r=5`, so

`5^(2)+h^(2)=6^(2)`

`\rightarrow 25+h^(2)=36`

`\rightarrow h^(2)=11`

`\rightarrow h=√(11)`

Answer 2

(a) 10π cm

(b) r = 5 cm

(c) h = √11 cm

Explanation:

(a) The surface of the opening the cup is circular in shape and a sector is cut from circle is calculate by formula,

C = r × θ

here, r = 6 cm

and θ =
`(5\pi)/(3)`

⇒
`C = 6 * (5\pi)/(3) = 10\pi`

(b) For finding the radius of the cup,

As the circumference of the circle is 10π

and we know that area of cone is calculate by formula, 2πr

⇒ 2πr = 10π

⇒ r = 5 cm

(c) In cone we know slant height(l) = 6 cm

Radius = 5 cm

Thus, using Pythagoras theorem,

l² = h² + r²

⇒ h² = l² - r²

⇒ h² = 36 - 25

⇒ h = √11 cm