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
$5^{2}+h^{2}=6^{2}$
$\rightarrow 25+h^{2}=36$
$\rightarrow h^{2}=11$
$\rightarrow h=\sqrt{11}$

Answer 2

Answer:

(a) 10π cm

(b) r = 5 cm

(c) h = √11 cm

Step-by-step 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 = $\frac{5\pi}{3}$

⇒ $C = 6 \times \frac{5\pi}{3} = 10\pi$

(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