Ex.13.3 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

Find the total surface area of a cone, if its slant height is \(21\,\rm m\) and diameter of its base is \(24 \,\rm m.\)

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-3 | Question 2

Text Solution

Reasoning:

The total surface area of the cone is the sum of the curved surface area and area of the base which is a circle.

What is known?

Diameter of the box and slant height of the cone.

What is unknown?

Total surface area of the cone.

Steps:

Total surface area of the cone is

\(= \pi rl + \pi {r^2} = \pi r(l + r) \)

Where \(l\) is slant height and radius \(r.\)

Diameter \(= 2r = 24 \rm\,m\) 

\(r = 12{\rm m}\\ \\ l = 21 \rm m\)

T S A \(= \pi r(l + r) \)

\(\begin{align} &= \frac{{22}}{7} \times 12 \times (12 + 21)\\ &= \frac{{22}}{7} \times 12 \times 33 \\ &= \frac{{8712}}{7} = 1244.57\,\,{\rm{m}}^2 \end{align}\)

Answer:

Total surface area of the cone \(\begin{align} = 1244.57\,{\rm{m}}^2 \end{align}\)