The perimeter of the base of a cone is 44 cm and the slant height is 25 cm. Find the volume and the curved surface of the cone.

Given, circumference of base = 44 cm.

⇒ 2πr = 44

$\Rightarrow 2 \times \dfrac{22}{7} \times r = 44 \\[1em] \Rightarrow r = \dfrac{44 \times 7}{2 \times 22} \\[1em] \Rightarrow r = \dfrac{44 \times 7}{44} \\[1em] \Rightarrow r = 7 \text{ cm}.$

Given, l = 25 cm.

We know that,

    l² = r² + h²
⇒ 25² = 7² + h²
⇒ h² = 25² - 7²
⇒ h² = 625 - 49
⇒ h² = 576
⇒ h = $\sqrt{576}$ = 24 cm.

Volume of cone = $\dfrac{1}{3}πr^2h$

Putting values in equation we get,

Volume of cone = $\dfrac{1}{3} \times \dfrac{22}{7} \times (7)^2 \times 24$

= $\dfrac{22 × 49 × 24}{3 \times 7}$

= 22 × 7 × 8 = 1232 cm³.

Curved surface area = πrl.

Putting values in equation we get,

Curved surface area = $\dfrac{22}{7} \times 7 \times 25$ = 22 × 25 = 550 cm².