NCERT Exemplar Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.4 in Chapter 13 - Surface Areas and Volumes
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A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m
(i) How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?
(ii) Find the volume of the cone.
According to the question,
Area of cloth = 165m2
Radius of conical tent = 5m
Area covered by 1 student = 5/7 m2
Curved surface area of cone = πrl
Thus, curved surface area of a conical; tent = πrl
\begin{array}{l} \Rightarrow 165=\frac{22}{7} \times 5 \times 1 \\ \Rightarrow 1=\frac{165 \times 7}{22 \times 5}=\frac{21}{2}=10.5 \mathrm{m} \end{array}
(i)
ii) Height of a cone,
r2 + h2 = l2
Where,
r=radius of a cone
h=height of a cone
l=slant height of a cone
⇒ (5)2 + h2 = (10.5)2
⇒ 25+ h2 = 110.25
⇒ h2 = 110.25 – 25 = 85.25
⇒ h = √85.25 = 9.23 m
Volume of a come = (1/3) πr2h
\text { Volume of a cone }=\frac{1}{3} \times \frac{22}{7} \times 5^{2} \times 9.23=\frac{5076.5}{21}=241.73 \mathrm{m}^{3}
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