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
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