Question

A tent has cylindrical surmounted by a
conical roof. The radius of the cylindrical
base is 20m.
The total height of tent is 6.3m and height
of cylindrical portion is 4.2m, find the
volume and surface area of tent.​

Answer 1

Answer:

volume = 6160m³ and surface area = 1792m²

Step-by-step explanation:

Given:

radius(r) = 20m

total height of the tent, (h)= 6.3m

height of cylinder, (h1) = 4.2m

Therefore, height of the cone (h2)= total height - height of cylinder

h2= h - h1 = 6.3 - 4.2= 2.1m

Now,

Total volume of the tent = area of the cylindrical portion + area of the conical portion

V = πr²h1 + 1/3 πr²h2

V = (22/7 × 20² × 4.2) + (1/3 × 22/7 × 20² × 2.1)

V = (8800 × 0.6 ) + (8800 × 0.1 )

V = 5280 + 880

V = 6160 cm³

To find the total surface area of the tent :

slant height of the cone, l = √(h² + r² )

= √((20)² + (2.1)²)

= √( 400 + 4.41 )

= √( 404.41)

= 20.11 m

Now,

Surface area of the tent = curved surface area of conical portion + curved surface area of cylindrical portion

= πrl + 2πrh

= (22/7 × 20 × 20.11) + (2× 22/7 × 20 × 4.2)

= ( 8,848.4/7 )+ (44× 20 × 0.6)

= 1264.06 + 528

= 1792 m²

Hope this helps!! Good luck !₍ᐢ.ˬ.ᐢ₎