A solid consists of a cone and a hemisphere which share a common base. The cone has
height of 6cm and base radius 4cm. Find volume and total surface area
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A solid consists of a cone and a hemisphere which share a common base. The cone has
height of 6cm and base radius 4cm. Find volume and total surface area
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Given :-
To Find :-
Formulae used:-
How to solve ?
Now,
→ Volume of cone = ⅓πr²h
→ ⅓ × 22/7 × 4 × 4 × 6
→ 22/7 × 4 × 4 × 2
→ 704/7
→ 100.57cm³
Now,
→ Volume of hemisphere = 2/3πr³
→ 2/3 × 22/7 × 4 × 4 × 4
→ 2816/21
→ 134.09cm³
Therefore,
→ Volume of solids = 100.57 + 134.09
→ Volume of solid = 234.66cm³
Now,
→ We have to find the slant height
→ using Pythogoras thereom
→ r² + h² = l²
→ (4)² + (6)² = l²
→ 16 + 36 = l²
→ 52 = l²
→ l = 7.21cm
Therefore,
→ C. S. A of cone = πrl
→ 22/7 × 4 × 7.21
→ 90.65cm²
Now,
→ C. S. A of hemisphere = 2πr²
→ 2 × 3.14 × 4 × 4
→ 100.48cm²
Therefore,
→ T. S. A of shape = 100.48 + 90.65
→ T. S . A of shape = 191.13cm²
Hence, The Total surface area of solid is 191.13cm²
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where,
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Radius of cone, r = 4 cm
Radius of hemisphere, r = 4 cm
Height of cone, h = 6 cm
So,
─━─━─━─━─━─━─━─━─━─━─━─━─━
☆Radius of cone, r = 4 cm
☆Radius of hemisphere, r = 4 cm
☆Height of cone, h = 6 cm
▪︎Slant height of cone, is given by
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More information :-
Perimeter of rectangle = 2(length× breadth)
Diagonal of rectangle = √(length²+breadth²)
Area of square = side²
Perimeter of square = 4× side
Volume of cylinder = πr²h
T.S.A of cylinder = 2πrh + 2πr²
Volume of cone = ⅓ πr²h
C.S.A of cone = πrl
T.S.A of cone = πrl + πr²
Volume of cuboid = l × b × h
C.S.A of cuboid = 2(l + b)h
T.S.A of cuboid = 2(lb + bh + lh)
C.S.A of cube = 4a²
T.S.A of cube = 6a²
Volume of cube = a³
Volume of sphere = 4/3πr³
Surface area of sphere = 4πr²
Volume of hemisphere = ⅔ πr³
C.S.A of hemisphere = 2πr²
T.S.A of hemisphere = 3πr²