Question

find the total surface area of a cone if it's slant height is 21 m and diameter of its base is 24 cm​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• Slant height of the cone = 21 m

• Diameter of the base of cone = 24 m

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• TSA of the cone

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Diameter = 24 cm

• Radius = ?

• $\sf Radius \: = \: \dfrac{Diameter}{2}$

• Slant height = 21 m

Substituting the values,

• $\sf Radius \: = \: \dfrac{24}{2}$

• Radius = 12 cm

We know that,

$\boxed{\pink{\sf TSA \: of \: the \: cone \: = \: \pi r(r \: + \: l) \: units^2}}$

Substituting the values,

• $\sf TSA \: of \: the \: cone \: = \: \dfrac{22}{7} \: * \: 12 \: (12 \: + \: 21) \: m^2$

• $\sf TSA \: of \: the \: cone \: = \: 3.14 \: * \: 12 \: (33) \: m^2$

• $\sf TSA \: of \: the \: cone \: = \: 3.14 \: * \: 12 \: * \: 33 \: m^2$

• $\sf TSA \: of \: the \: cone \: = \: 1243.44 \: m^2$

Therefore,

• TSA of a cone = 1243.44 m².

$\Large{\bf{\purple{\mathfrak{\dag{\underline{\underline{Note:-}}}}}}}$

• There's a mistake in the question, diameter of the base of cone is 24 m and not 24 cm.

Answer 2

Given :

• Slant height = 21 m
• Diameter of its base = 24 cm

To Find :

• Total surface area of a cone

Solution :

We know that, Diameter = 24cm

First we have to find the radius,

⇒ Radius = Diameter / 2

⇒ Radius = 24 / 2

⇒ Radius = 12m

We have, π = 22/7 , r = 12m , l = 21

By using formula,

⇒ TSA of cone = πr(r+l)

⇒ TSA of cone = 22/7 × 12 ( 12 + 21 )

⇒ TSA of cone = 22/7 × 12 × 33

⇒ TSA of cone = 8712 / 7

⇒ TSA of cone = 1244.57m³

•°• Total surface area of a cone = 1244.57m³

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