A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7cm. and it's volume is 3/2 of the hemisphere. calculate the height of the cone and the surface area of the toy.
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Radius of cone and hemisphere = 7 cm
Height of cone be h cm
Now, volume of hemisphere = (2/3)πr³
Volume of cone = (1/3)πr²h
A/q
(1/3)πr²h = (3/2)×[(2/3)πr³]
⇒h = 3r = 3×7 = 21 cm
Now, surface area
Slant height, l = √[(21)² +(7)²] = 7√10 cm = 22.13
Total surface area = (curved surface area of cone + hemisphere)
= (πrl + 2πr²)
=[(22/7)×7×22.13) + 2(22/7)×(7)²]
= 486.86 +308
=794.86 cm²
Height of cone be h cm
Now, volume of hemisphere = (2/3)πr³
Volume of cone = (1/3)πr²h
A/q
(1/3)πr²h = (3/2)×[(2/3)πr³]
⇒h = 3r = 3×7 = 21 cm
Now, surface area
Slant height, l = √[(21)² +(7)²] = 7√10 cm = 22.13
Total surface area = (curved surface area of cone + hemisphere)
= (πrl + 2πr²)
=[(22/7)×7×22.13) + 2(22/7)×(7)²]
= 486.86 +308
=794.86 cm²
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