Question

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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Answer 1

$\huge \dag \Large \underline \frak \red{Question}$

↝ 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.

$\huge \dag \Large \underline \frak \red{Solution}$

✒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

Answer 2

ANSWER

✒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