Question

hey guys,

plzz answer this fast

The interior of a building is in the form of cylinder of diameter 4m and height 3.5m surmounted by cone of same radius with vertical right angle .Find surface area and volume of interior of build.

Answer 1

$\color{red}\huge\bold\star\underline\mathcal{Hey\:Mate}\star$

Here is your answer... ☺️☺️☺️
➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡➡

Solution :-

Diameter of the cylindrical portion = 4.3 m

Radius = 4.3/2 = 2.15 m

Height = 3.8 m

Lateral Surface Area of cylindrical portion = 2πeh

⇒ 2*22/7*2.15*3.8

= 359.48/7

= 51.3543 m²

It is mentioned that vertical angle of the cone is a right angle.

Let BAC be the triangle.

In Δ BAC,

Slant height 'l' = AB = AC

⇒ l² + l² = (BC)²  (BC = diameter of the common base of cone and cylinder)

⇒ 2l² = (4.3)²

⇒ 2l² = 18.49

⇒ l² = 18.49/2

⇒ l² = 9.245

⇒ l = 3.04 m

So, slant height is 3.04 m

l² = r² + h²
 
(3.04)² = √(2.15)² + h²

9.2416 = 4.6225 + h²

h² = 9.2416 - 4.6225

h² = 4.6191

h = √4.6191

h = 2.149  or 2.15 m (Approx) 

Lateral surface area of conical portion = πrl

22/7*2.15*3.04

143.792/7

= 20.5417 m²

Total surface area of the building = Surface area of cylindrical portion + Surface area of the conical portion

⇒ 51.3543 + 20.5417

= 71.896 m² 

Volume of Cylindrical portion = πr²h

22/7*2.15*2.15*3.8

386.441/7

= 55.2059 m³

Volume of the conical portion = 1/3πr²h

1/3*22/7*2.15*2.15*2.15

218.64425/21

= 10.4116 m³

Total volume of the building = Volume of the cylindrical portion + Volume of the conical portion

55.2059 + 10.4116 

= 65.6175 m³

Answer.

✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔
I hope this answer is helpful to u...❤❤❤

Keep Asking... ✌️✌️✌️

✨✨✨If help u. Mark my answer as brainliest✨✨✨

$<font color="red"><marquee>❤️❤️❤️Thank You❤️❤️❤️</marquee></font>$