NCERT Exemplar Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.4 in Chapter 13 - Surface Areas and Volumes

Question 3 Surface Areas and Volumes - Exercise 13.4

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,

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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