Question

A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.

Answer 1

Answer:

capacity of the tent = 500 π m³ &  cost of the canvas is  ₹ 55000.

Step-by-step explanation:

SOLUTION :  

Given :  

Diameter of the cylinder = 20 m

Radius of the cylinder = Radius of the cone ,r = 10 m

Height of the cylinder , H  = 2.5 m

Height of the Cone , h =7.5 m

Slant height of the cone , l = √r² + h²

l = √10² + 7.5² = √100 + 56.25 = √156.25  

l = 12.5 m

Capacity of the tent = Volume of cylinder + volume of cone

= πr²H + ⅓ × πr²h

= πr²(H + ⅓ × h)

= π × 10² (2.5 + ⅓ × 7.5)

= 100π (2.5 + 2.5)

= 100 π × 5 = 500 π  

V1 = 500 π m³.

capacity of the tent = 500 π m³.

 

Total area of the canvas required for the tent ,S = curved surface area of cylinder +  curved surface area of cone

S = 2πrH + πrl

S = 2(π)(10)(2.5) + π(10)(12.5)

S = 50π + 125π

S = π(50 + 125) = π × 175 = 22/7 × 175 = 22 × 25

S = 550 m²

Total cost of the canvas  = Total area of the canvas × Rate  

=  (100) (550) = ₹ 55000

Total cost of the canvas  = ₹ 55000

Hence, Total capacity of the tent = 500 π m³ &  Total cost of the canvas is  ₹ 55000.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\huge\bf\pink{\mid{\overline{\underline{Your\: Answer}}}\mid}$

capacity of the tent = 500 π m³

 cost of the canvas is  ₹ 55000.

Step-by-step explanation:

Given,

Diameter of the cylinder = 20 m

and,

Radius of the cylinder = Radius of the cone ,r = 10 m

also,

Height of the cylinder , H  = 2.5 m

and,

Height of the Cone , h =7.5 m

now,

Slant height of the cone , l = √r² + h²

=> l = √10² + 7.5² = √100 + 56.25 = √156.25  

=> l = 12.5 m

now,

Capacity of the tent = Volume of cylinder + volume of cone

= πr²H + ⅓ × πr²h

= πr²(H + ⅓ × h)

= π × 10² (2.5 + ⅓ × 7.5)

= 100π (2.5 + 2.5)

= 100 π × 5 = 500 π  

therefore,

capacity of the tent = 500 π m³.

again,

Total area of the canvas required for the tent ,S = curved surface area of cylinder +  curved surface area of cone

=> S = 2πrH + πrl

=> S = 2(π)(10)(2.5) + π(10)(12.5)

=> S = 50π + 125π

=> S = π(50 + 125) = π × 175 = 22/7 × 175 = 22 × 25

S = 550 ${m}^{2}$

therefore,

Total cost of the canvas  = Total area of the canvas × Rate  

=  (100) (550) = ₹ 55000

so,

Total cost of the canvas  = ₹ 55000

Hence,

Total capacity of the tent = 500 π m³

and

Total cost of the canvas is  ₹ 55000