a tent is in the form of cylinder of a diameter 4.3 m and height 3.8 m surmounted by a cone whose vertical angle is a right angle. find the TSA and the volume of the tent
Answers
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 m
HOPE IT HELPS!!!
MARK IT AS THE BRAINLIEST
SOLUTUON :
Given :
π = 3.14.
Vertical angle of cone is a right angle.
Diameter of Cylinder = 4.3m.
Height of Cylinder = 3.8m.
So, Radius of Cylinder = 4.3/2 = 2.15m.
To Find : TSA. and Volume of the tent.
Now, TSA. of the tent = CSA. of cylinder + CSA. of cone.
CSA. OF CYLINDER = 2πrh.
2πrh = 2 × 3.14 × 2.15 × 3.8 = 51.3076m².
Now, Slant Height ( L ) of cone = AB = AC.
Let ABC be the triangle.
Now,
B² = P² + H².
BC² = AC² + AB².
BC² = L² + L².
BC² = 2L².
(4.3)² = 2L².
18.48 = 2L².
18.49/2 = L².
√9.245 = L.
3.04m = L.
Now,
L² = R² + H².
(3.04)² = (2.15)² + H².
9.2416 = 4.6225 + H².
9.2416 - 4.6225 = H².
√4.6191 = H.
2.149m = 2.15m (approx.).
CSA. OF CONE = πrl.
3.14 × 2.15 × 3.04 = 20.5230m².
So,
TSA. of the tent = CSA. of cylinder + CSA. of cone.
51.3076 + 20.5230 = 71.83m².
THEREFORE, TOTAL SURFACE AREA OF THE TENT IS 71.83m².
Now, Volume of tent = Volume of cylinder + Volume of Cone.
VOLUME OF CYLINDER = πr²h.
3.14 × (2.15)² × 3.8.
3.14 × 4.6225 × 3.8.
55.15567m³.
VOLUME OF CONE = 1/3π²h.
1/3 × 3.14 × (2.15)² × 2.15.
1/3 × 3.14 × 4.6225 × 2.15.
1/3 × 31.20532.
10.40177m³.
Now,
Volume of tent = Volume of cylinder + Volume of Cone.
55.15567 + 10.40177 = 65.5m³.
THEREFORE, VOLUME OF THE TENT IS 65.5m³.
《I HOPE YOU UNDERSTOOD MY EXPLANATION AND IT HELPED YOU IN THE BEST WAY ^^ HAVE A GOOD SLEEP TONIGHT!! 》