Math, asked by harinichimbili, 8 months ago


A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and
the diameter of the cylinder is 7 cm. Then the volume and total surface area of the solid is




who ever answer it first and correctly i will mark as a branlist ​

Answers

Answered by DrNykterstein
22

Given that, A solid is in the form of a cylinder whose two ends are Hemisphere.

➜ Total height of the solid, h = 19 cm

➜ Diameter of the cylinder is 7 cm.

Here, The radius of the two hemispheres is 7/2 cm because the radius of the cylinder is given as 7/2 cm.

Since, The solid consists of 1 cylinder and two hemispheres

∴ Actual height of the cylinder = Total height - 2 × radius of hemispheres

h = 19 - 2 × 7/2

h = 19 - 7

h = 12 cm

Now, We need to find the volume and total surface area of the solid.

⇒ Volume of Solid = Volume of Cylinder + 2 × Volume of one hemisphere

⇒ V = πr²h + 2 ( 2πr³ / 3 )

⇒ V = πr²h + 4πr³ / 3

⇒ V = πr² ( h + 4r / 3 )

⇒ V = πr² / 3 ( 3h + 4r )

Substituting values,

⇒ V = ( π × 7/2 × 7/2 ) × 1/3 ( 3×12 + 4×7/2 )

⇒ V = 77 / 6 × ( 36 + 14 ) [ take, π = 22/7 ]

⇒ V = 77 × 50 / 6

V = 641.666...

⇒ V ≈ 641.67 cm³

Also,

⇒ Surface Area of Solid = CSA of Cylinder + 2 × CSA of Hemisphere

⇒ SA = 2πrh + 2×2πr²

⇒ SA = 2πr ( h + 2r )

Substituting values,

⇒ SA = 2×22/7×7/2 ( 12 + 2×7/2 ) [ take, π = 22/7 ]

⇒ SA = 22 × 19

SA = 418 cm²

Hence, Volume of Solid is 641.67 cm³ and the Surface Area is 418 cm²

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