Question

A solid toy is in the form of hemisphere surmounted by a Right circular cone of same radius

Answer 1

Cylinder Covers 25.12 $cm^3$ More Space

Step-by-step explanation:

The Complete Question is -

A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.

Volume of toy = Volume of cone + Volume of hemisphere ""(1)

We know that,

• Volume of Cone = $\frac {1}{3} \pi r^2 h$

• Volume of Hemisphere = $\frac {2}{3} \pi r^3$

So, Putting the above two formulas in (1) equation we get-

• Volume of Toy = $\frac {1}{3} \pi r^2[H+2r]h$

= $\frac {1}{3} \times \frac {22}{7} \times 2 \times \times 2[2+2 \times 2]$

= $\frac {1}{3} \times \frac {22}{7} \times 4 \times 6^2$

= 25.12 $cm^3$

• Volume of Cylinder = $\pi r^2 h$

= $\frac {22}{7} \times 2 \times \times 2[2+2]$

= $\frac {22}{7} \times 16$

= 50.24 $cm^3$

• Difference in Volume = Volume of Cylinder - Volume of Toy

50.24 - 25.12 = 25.12 $cm^3$

Hence, Cylinder Covers 25.12 $cm^3$ more space.