Question

Find the volume of a cone whose circumference of base is 16 cm and height is 3 cm.​

Answer 1

Given :

• Circumference of a cone = 16 cm
• Height of a cone = 3 cm

To find :

• Volume of the cone

Solution :

Firstly, from the formula of circumference we will find the value of the radius.

Using formula,

Circumference = 2πr

where,

• Take π = 22/7
• r = radius

Substituting the given values,

⇒ 16 = 2 × 22/7 × r

⇒ 16 = 44/7 × r

⇒ (16 × 7)/44 = r

⇒ 112/44 = r

⇒ 2.55 = r

Radius = 2.55 cm

Using formula,

Volume of cone = 1/3 πr² h

where,

• Take π = 22/7
• r = radius
• h = height

Substituting the given values,

⇒ Volume = 1/3 × 22/7 × 2.55 × 2.55 × 3

⇒ Volume = 429.165/21

⇒ Volume = 20.43

Volume of cone = 20.43 cubic centimeter.

__________________________

Some related formulae -

• Area of circle = πr²
• Volume of cylinder = πr²h
• Total surface area of cylinder = 2πrh + 2πr²
• Total surface area of cone = πrl + πr²h
• Curved surface area of cone = πrl
• Diameter = 2 × radius
• Radius = Diameter/2

Answer 2

Circumference of base of the cone = 16 cm

Height of the cone = 3 cm

Now, by using the formula, circumference of circle = 2πr

• 16 = 2 × $\dfrac{22}{7}$ × r

• $\dfrac{16×7}{2×22}$ = r

• r = $\dfrac{112}{44}$

• r = 2.54545 cm

Now, volume of the cone = $\dfrac{1}{3}$ πr²h

• $\sf V_{cone}$ = $\dfrac{1}{3}$ × $\dfrac{22}{7}$ × 2.54 × 2.54 × 3

• $\sf V_{cone}$ = $\dfrac{22×6.4516×3}{21}$

• $\sf V_{cone}$ = $\dfrac{425.80}{21}$

• $\sf V_{cone}$ = 20.27 cm³

$\bold{Hope\;it \; helps\;!}$