Question

The figure alongside is a cylinder with a hemispherical
end. Calculate


(i) the total surface area of the solid,

(ii) the volume of the solid.​

Answer 1

Given :-

• Height of the cylinder = 40 cm
• Radius of the cylinder = 10.5 cm

To find :-

• The total surface area of the solid
• The volume of the solid

Formula :-

• Volume of a cylinder = πr²h
• Volume of a hemisphere = 2/3πr³
• Surface area of cylinder = 2πrh
• Surface area of hemisphere = 2πr²

Answer :-

Radius of the cylinder = radius of the hemisphere

[ Since , both are attached to one another so both will have the same radius ]

Therefore, radius of the hemisphere = 10.5 cm

(i) The total surface area of the solid

=?

Total surface area = Surface area of cylinder + surface area of the hemisphere + area of the circle

➡ Total surface area = 2πrh + 2πr² + πr²

➡ Total surface area = πr ( 2h + 2r + r)

➡ Total surface area = 22/7 × 10.5 ( 2×40 + 2×10.5 + 10.5 )

➡ Total surface area = 22/7 × 10.5 ( 80 + 21 + 10.5 )

➡ Total surface area = 22/7 × 10.5 × 111.5

➡ Total surface area = 3679.5 cm²

(ii) The volume of the solid = ?

Volume of the solid = Volume of the cylinder + volume of the hemisphere

➡ Volume of the solid = πr²h + 2/3πr³

➡ Volume of the solid = πr² ( h + 2/3 × r)

➡ Volume of the solid = 22/7 × 10.5 × 10.5 ( 40 + 2/3 × 10.5 )

➡ Volume of the solid = 22/7 × 110.25 ( 40+7 )

➡ Volume of the solid = 22/7 × 110.25 × 47

➡ Volume of the solid = 16285.5 cm³

Therefore , the total surface area of the solid is 3679.5 cm² and the total volume of the solid is 16285.5 cm³

Answer 2

Answer:

A hollow cylindrical iron pipe with external and internal radii 8 cm and 6 cm respectively and length 35 cm is melted and recast into a solid wire of thickness 2.8 cm. Find the length of the wire.6686

Step-by-step explanation: