Question

The internal and external radii of a hollow sphere are 3 cm and 5 cm respectively. The sphere is melted to form a solid cylinder of height 2 2/3 cm.find the diameter and curved surface area of cylinder

Answer 1

vol of hollow sphere = vol of cylinder

Answer 2

The diameter and curved surface area of cylinder are 14 cm and 117.33 sq.cm. respectively.

Step-by-step explanation:

Internal Radius of sphere = 3 cm

External radius of sphere = 5 cm

Height of cylinder = $2\frac{2}{3} = \frac{8}{3} cm$

We are given that The sphere is melted to form a solid cylinder

Volume of sphere = Volume of cylinder

$\frac{4}{3} \pi (R^3-r^3)=\pi r^2 h\\\frac{4}{3}(5^3-3^3)=\frac{8}{3}r^2\\(5^3-3^3)=2r^2\\\sqrt{\frac{(5^3-3^3)}{2}}=r$

7=r

Diameter of cylinder = 2r =2(7)= 14 cm

Curved surface area of cylinder =$2 \pi r h = 2 \times \frac{22}{7} \times 7 \times \frac{8}{3}=117.33sq.cm.$

Hence  the diameter and curved surface area of cylinder are 14 cm and 117.33 sq.cm. respectively.

#Learn more:

The internal and external radii of a hollow sphere are 3cm and 5cm .the sphere is melted to form a cylinder of height 22/3 cm.find C.S.A of cylinder

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