Question

From a solid cylinder whos hight is 40cm and diameter 18cm a conical cavity of the same height and same diameter is hallowed out find the total surface of remaining solid

Answer 1

Gɪᴠᴇɴ :-

• Height = 40cm.
• Diameter = 18cm.
• a conical cavity of the same height and same diameter is hallowed out .

Tᴏ Fɪɴᴅ :-

• find the total surface of remaining solid ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• CSA of cylinder = 2πrh
• Slant height of cone = √(r² + h²)
• CSA of cone = πrL
• Total Surface Area of the Remaining solid = The outer surface area of the cylinder + inner surface area of the Hollow portion of the cylinder left + surface area of the cylindrical base..

Sᴏʟᴜᴛɪᴏɴ :-

→ The Outer surface area of the cylinder = 2πrh

→ 2 x 3.14 x 9 x 40

→ 2260.8 cm²

Now, Slant Height of the cone, L = √(h² + r²)

→ √(40² + 9²)

→ √(1600+81)

→ √1681

→ 41 cm

So, Outer surface area of the cone = πrL

→ 3.14 x 9 x 41

→ 1158.66 cm²

This outer surface area of the cone is equal to the inner surface area of the hollow portion of the cylinder left.

And, surface area of the cylindrical base = πr²

→ 3.14 x 9²

→ 3.14 × 81

→ 254.34 cm²

Therefore, Total Surface Area of the Remaining solid = The outer surface area of the cylinder + inner surface area of the Hollow portion of the cylinder left + surface area of the cylindrical Base.

→ 2260.8 + 1158.66 + 254.34

→ 3673.8 cm² (Ans.)

Hence The Total Surface Area of the Remaining solid will Be 3673.8 cm²..

Answer 2

$\rule{200}4$

$\huge\tt{PROBLEM:}$

• From a solid cylinder whos hight is 40cm and diameter 18cm a conical cavity of the same height and same diameter is hallowed out find the total surface of remaining solid

$\rule{200}2$

$\huge\tt{CONCEPT~USED:}$

• CSA of a cylinder = 2πrh
• Slant height of a cone = √{r² + h²}
• CSA of a cone = πrl
• TOTAL SURFACE AREA OF THE REMAINING SOLID = outer surface of the cylinder + inner surface of the hollow portion of Cylinder + surface area of Cylindrical base

$\rule{200}2$

$\huge\tt{SOLUTION:}$

➡️The outer surface area of Cylinder = 2πrh

➡️The outer surface area of Cylinder =2×3.14×9×40

➡The outer surface area of Cylinder =️2260.80 cm²

$\rule{200}2$

➡️Slant Height of the cone = √(h²+r²)

➡Slant Height of the cone = ️√{40²+9²}

➡Slant Height of the cone = ️√{1600+81}

➡️Slant Height of the cone = √1681

➡Slant Height of the cone = ️41 cm

$\rule{200}2$

➡️Outer surface area of the cone = πrl

➡Outer surface area of the cone = ️3.14 × 9 × 41

➡Outer surface area of the cone = ️1158.66 cm²

$\rule{200}2$

➡️ Surface area of the Cylindrical base = πr²

➡️3.14 × 9²

➡️3.14 × 81

➡️254.34 cm²

$\rule{200}2$

➡️Total surface area = outer surface of the cylinder + inner surface of the hollow portion of Cylinder + surface area of Cylindrical base

➡️Total surface area =

2260.8 + 1158.66 + 254.34

➡Total surface area =️3673.8 cm²

$\rule{200}4$