Question

★Moderators
★Stars
★Best Users

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.
$\bf\mathbb{NOTE :}$
- No spam!
- No copy paste!​

Answer 1

Step-by-step explanation:

$\sf \: Radius \: of \: cone, \: r=7cm \\ \sf \: Volume \: of \: cone = \frac{3}{2} \\ \sf \: volume \: of \: hemisphere \: \\ \sf = \frac{1}{3} \pi \: {r}^{2} h = \frac{3}{2} \times \frac{2}{3} \pi \: {r}^{3} \\\sf⇒h=3r=3×7=21cm$

$\sf \purple{Surface \: area \: of \: the \: toy  \: = curved \: } \\ \sf \blue{Surface \: area \: of \: the cone  \: +  \: curved} \\ \sf \pink{Surface \: area \: of \: the \: hemisphere.} \\ \sf \red{Radius \: of \: cone, \: r \: =7cm} \\ \sf \green{Height \: of \: cone, \: h \: =21cm}$

$\sf \: Slant \: height \:  =l \: = \sqrt{ {r}^{2} + {h}^{2} } \\ \sf \: = \sqrt{ {7}^{2} + {21}^{2} } = \sqrt{49 + 441} = 490 = 22.135 \\ \sf \: Curved \: surface \: area =πrl \\ \sf \: = \frac{22}{7} \times 7 \times 22.135 = 486.99 {cm}^{2} \\ \sf \: Curved \: surface \: area \: of \: the \: toy  \: \\ \sf=486.99 \: +308=794.99 {cm}^{2}$