Question

a cylinder is open at one end the external diameter is 10 centimetre and thickness 2 centimetre the height is 8 cm find capacity of cylinder and volume of metal used

Answer 1

Hello!

A cylinder is open at one end the external diameter is 10 centimetre and thickness 2 centimetre the height is 8 cm find capacity of cylinder and volume of metal used

Data:

h (height) = 8 cm

De (external diameter) = 10 cm

radius (external diameter)

De = 2*r → 2r = D → r = De/2 → r = 10/2 → r (radius) = 5 cm

di (internal diameter) = ?

th (thickness) = 2 cm

Total Volume of cylinder:

$Vtc = h* \pi *r^2$

$Vtc = 8*3.14*5^2$

$Vtc = 8*3.14*25$

$\boxed{Vtc = 628\:cm^3}$

$De = di + 2*th$

$10 = di + 2*2$

$10 = di + 4$

$di = 10 - 4$

$di = 6 cm$

radius (internal diameter)

Di = 2*r → 2r = Di → r = Di/2 → r = 6/2 → r (radius) = 3 cm

Volume of metal used:

$Vm = h* \pi *r^2$

$Vm = 8*3.14*3^2$

$Vm = 8*3.14*9$

$\boxed{\boxed{Vm = 226.08\:cm^3}}\end{array}}\qquad\quad\checkmark$

Find capacity of cylinder: (internal volume)

To find the capacity of the cylinder, we subtract the total volume value of the cylinder minus the volume value of the metal

$V_{cc} = V_{tc} - V_{m}$

$V_{cc} = 628 - 226.08$

$\boxed{\boxed{V_{cc} = 401.92\:cm^3}}\end{array}}\qquad\quad\checkmark$

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I Hope this helps, greetings ... DexteR ! =)

Answer 2

Height = 8cm
external diameter= 10cm
external Radius= 10/2
                           = 5cm
Thickness= 2cm
Internal Radius = External Radius - Thickness
                           = 5cm - 2cm
                           = 3cm

Capacity of cylinder (Radius used here is Internal radius)
$\pi$ × r² × h
$\pi$ × 3² × 8
$\pi$ × 9 × 8
$\pi$ × 72cm²
226cm³

Entire cylinder's volume - internal cylinder's volume = external cylinders volume
volume of metal used = external cylinder's volume

entire cylinder's volume
$\pi$ × R²×h
$\pi$ × 5² ×8
$\pi$ × 25 × 8
$\pi$ ×200cm²
628cm³

Volume of Internal cylinder
226cm³

Volume of metal used
External volume - Internal volume = Volume of metal used
628 - 226
402cm³


Ans (i) 226cm³  (ii) 402cm³

Hope it helps :)