A container shaped like a right circular cylinder has a diameter 12 cm and height 15 cm is full of ice cream.The ice cream is to be filled into 10 equal cones having a hemispherical shape on the top. If the height of the cone is 4 times its radius, then find the height of the cone.
(Class 10 Maths Sample Question Paper)
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SOLUTION:
Given:
Diameter of a cylinder = 12 cm
Height of the cylinder (h) = 15 cm
Radius of cylinder(r) = 12/2= 6 cm
Volume of Cylinder = πr²h = π (6)²(15)= π×36×15 = 540π cm³
Let the radius of the cone be r1 cm.
Height of the cone (h1) = 4 × radius of cone = 4r1
Volume of a cone with hemispherical part= ⅓(πr1²h1) + ⅔(πr³)
= 1/3πr1²(4r1) + ⅔(πr³)
= 2πr1³ cm³
Volume of the cylinder= 10× volume of cone with hemisphere
540 π= 10 × 2πr1³
540/10 = 2r1³
54/2 = r1³
27 = r1³
r1³ = 27
r1 =³√27
r1 = 3 cm
Hence, the height of the cone= 4r1= 4 × 3 = 12 cm.
HOPE THIS WILL HELP YOU...
Given:
Diameter of a cylinder = 12 cm
Height of the cylinder (h) = 15 cm
Radius of cylinder(r) = 12/2= 6 cm
Volume of Cylinder = πr²h = π (6)²(15)= π×36×15 = 540π cm³
Let the radius of the cone be r1 cm.
Height of the cone (h1) = 4 × radius of cone = 4r1
Volume of a cone with hemispherical part= ⅓(πr1²h1) + ⅔(πr³)
= 1/3πr1²(4r1) + ⅔(πr³)
= 2πr1³ cm³
Volume of the cylinder= 10× volume of cone with hemisphere
540 π= 10 × 2πr1³
540/10 = 2r1³
54/2 = r1³
27 = r1³
r1³ = 27
r1 =³√27
r1 = 3 cm
Hence, the height of the cone= 4r1= 4 × 3 = 12 cm.
HOPE THIS WILL HELP YOU...
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