Question

9
The ratio of the base area and the curved surface area of a conical ten
40:41. If its height is 18 m, find the air capacity of the tent in terms of​

Answer 1

Answer:

air capacity menas area of the tent use formula

Answer 2

Answer:

G I V E N :-

❥ The ratio of base area and CSA of a conical tent = 40:41

Step-by-step explanation:

➵ $\frac{ Base }{ CSA }$ = $\frac{ 40 }{ 41 }$

• Area of a comical tent = πr²
• CSA of conical tent = πr $\sqrt{ h² \: + \: r² }$

➵ $\frac{ πr² }{ πr √h² \: + \: r² }$ = $\frac{ 40 }{ 41 }$

➵ $\frac{ r }{ 18² \: + \: r² }$ = $\frac{ 40 }{ 41 }$

• Squaring on both sides

➵ $\frac{ r² }{ 18 \: + \: r² }$ = $\frac{ 40² }{ 41² }$

➵ $\frac{ r² }{ 18 \: + \: r² }$ = $\frac{ 1600 }{ 1681 }$

➵ 1681 r² = 1600 (18² + r²)

➵ $\frac{ 1681 }{ 1600 r² }$ = 324 + r²

➵ 1.050625 r² - r² = 324

➵ r² = $\frac{ 324 }{ 0.050625 }$

➵ r² = 6400

➵ r = √6400

➵ r = 80m

❥ Air capacity = ⅓ π r² h

• ⅓ × $\frac{ 22 }{ 7 }$ × 80 × 80 × 18
• 38,400 π cu m