Given,
The radius of cylinder=6cm
Height of cylinder=8cm
To find,
- Volume of the cylindrical shape formed
- Radius of a sphere formed by the same clay
- Difference b/w the curved surface area
- Volume of the sphere, if the radius of cylinder increased by 1 cm.
- Amount of colored paper required to wrap the cylinder.
Solution,
1. Volume of cylinder= πr²h
= π×6×6×8
= 288πcm³ (option b)
2. Radius of sphere=?
since, the cylinder is molded into a sphere,
therefore, the volume of the cylinder= volume of the sphere
⇒ πr²h=4/3πr³
⇒π×r×r×h=4/3×π×r×r×r
⇒h=4/3r
⇒8=4/3×r
⇒r=6cm. (option c)
3. The difference between the curved surface area of both the shapes
C.S.A of cylinder=2πrh
C.S.A of sphere=4πr²
⇒2πrh - 4πr² = 2×π×6×8 - 4×π×6×6
⇒144π - 96π = 48π
Therefore, difference=48πcm². (option c)
4. When the radius of the cylinder increased by 1cm
volume of sphere=1232cm³
5. Amount of colored paper required to wrap the cylinder
168πcm². ( option b )