Question

A cylinder of diameter 6cm is melted to form a cone 3.6cm high and 3m in diameter. Find the height of the cylinder.​

Answer 1

$\sf{diameter \: of \: cylinder = 6 \: cm}$

$\sf{radius \: of \: cylinder(R) = \frac{6}{2} = > 3cm}$

$\sf{height \: of \: cone (h)= 3.6 \: cm}$

$\sf{diameter \: of \: cone = 3 \: cm}$

$\sf{radius \: of \: cone(r)} = \frac{3}{2} = > 1.5cm$

$\red{\boxed{\sf \green{volume \: f \: cylinder = volume \: of \:cone}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \pi {R}^{2} H = \frac{1}{3} \pi {r}^{2} h}$

$\: \: \: {3}^{2} \times H = \frac{1}{3} \times {(1.5)}^{2} \times 3.6$

$\: \: \: \: \: \: \: \: \: \: H = \frac{2.25 \times 3.6}{3 \times 9}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{H = 0.3 \: cm}$

$\sf\orange{please\:mark\:as\:brainliest............}$

Answer 2

$\underline\bold\blue{Given}$

Diameter of cylinder = 6cm

Radius of cylinder = $\cancel\dfrac{6}{2}$ = 3

Height of cone = 3.6cm

Radius of cone = 1.5cm

$\underline\bold\blue{To find}$

Height of cylinder = ?

$\underline\bold\blue{Solution}$

Volume of cone = Volume of cylinder

$\dfrac{1}{3}$ πr²h = πr²h

$\rightarrow$$\dfrac{1}{3}$ × 1.5cm × 1.5cm × 3.6cm = 3cm × 3cm × h

$\rightarrow$3.6cm = 9h

$\rightarrow$$\cancel\dfrac{3.6}{9}$

$\rightarrow$H = 0.4 cm³