Question

a solid toy is in the form of a hemisphere surmounted by a right circular cylinder. the height of the cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy.
If a cube circumscribes the toy, then find the difference of the volume of the cube and the toy. Also, find the total surface area of the toy.

The main part is the cube one please solve that

Answer 1

SOLUTION

Given,

Height of the cone = 2cm

Height of the cone = 2cm& Diameter of the cone=4cm

So, radius of the cone = Radius of hemisphere= 4/2 = 2cm

Therefore,

Volume of the cone

$= > \frac{1}{3} \pi {r}^{2} h \\ = > \frac{1}{3} \times \pi \times {2}^{2} \times 2 \\ = > \frac{8}{3}\pi \: {cm}^{3}$

And,

Volume of the hemisphere

$= > \frac{2}{3} \pi {r}^{2} \\ = > \frac{2}{3} \times \pi \times {2}^{3} = \frac{16}{3} \pi \: cm {}^{3}$

Thus,

Total volume of the solid toy

=)volume of the cone+ volume of the hemisphere

$= > \frac{8}{3} \pi + \frac{16}{3} \pi \\ = > \frac{24}{3} \pi = 8\pi \: cm {}^{3}$

Now, Right circular cylinder

circumscribes the solid. so,

Radius of right circular cylinder CO=EF=2cm

& Height of right circular cylinder OO' =OP+PO'= 2+2= 4cm

Therefore,

Volume of right circular cylinder

$= > \pi {r}^{2} h = \pi {2}^{2} \times 4 = 16\pi$

Thus,

Volume of right circular cylinder- Volume of solid toy

=) 16π -8π = 8π

=) 8× 3.14 = 25.12cm^3

Hence, right circular cylinder is having 25.12 cm^3 more space than the solid.

hope it helps ☺️