Question

a cylinder of radius 6cm and height 10cm and a cone of radius 6cm and height 5cm is melted and a big cylinder of diameter 8cm is formed. find height of new cylinder with figure​

Answer 1

Answer:

• Height of new cylinder is 26.249 cm (approx).

Step-by-step explanation:

Concept :-

• Here we are melting the cone and cylinder. So, sum of their volume will be equal to Volume of big cylinder.

For cylinder:

Radius of cylinder is 6 cm.

Height of cylinder is 10 cm.

For cone :

Radius of cone is 6 cm.

Height of cone is 5 cm.

Volume of cylinder = πr² h

• Where, r and h are radius and height of cylinder.

Putting r and h in formula :

$\sf \longrightarrow \pi \times {(6)}^{2} \times 10 \\ \\ \sf \longrightarrow \dfrac{22}{7} \times 36 \times 10 \\ \\ \sf \longrightarrow \dfrac{7920}{7} \\ \\ \sf \longrightarrow \pink{\boxed{\sf \bold{1131.42}} \star}$

Volume of cylinder = 1131.42 cm³.

Volume of cone = $\sf \bold{\dfrac{1}{3} \pi r^{2} h}$

• Where, r and h are radius and height of cone.

Put r and h in formula :

$\sf \longrightarrow \dfrac{1}{3} \times \dfrac{22}{7} \times (6)^{2} \times 5 \\ \\ \sf \longrightarrow \dfrac{22}{21} \times 36 \times 5 \\ \\ \sf \longrightarrow \dfrac{3960}{21} \\ \\ \sf \longrightarrow \purple{\boxed{\sf \bold{188.57}}\star }$

Volume of cone is 188.57 cm³.

For big (new) cylinder :-

Diameter of cylinder is 8 cm

Radius = Diameter/2

Radius = 8/2 = 4

Radius of cylinder is 4 cm.

Let, h be the the height of cylinder.

Diagram of big (new) cylinder :-

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4 cm}}\put(9,17.5){\sf{h}}\end{picture}$

Volume of big (new) cylinder = Volume of cylinder + volume of cone

$\sf \longrightarrow \dfrac{22}{7} \times (4)^{2} \times h = 1131.42 + 188.57 \\ \\ \sf \longrightarrow \dfrac{22}{7} \times 16 \times h = 1319.99 \\ \\ \sf \longrightarrow \dfrac{352}{7} \times h = 1319.99 \\ \\ \sf \longrightarrow 352 \times h = 1319.99 \times 7 \\ \\ \sf \longrightarrow 352 \times h = 9239.93 \\ \\ \sf \longrightarrow h = \dfrac{9339.93}{352}\\ \\ \sf \longrightarrow \green{\boxed{\sf \bold{h=26.24}} \bigstar}$

Therefore,

Height of big (new) cylinder is 26.24 (approx).

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Concept :-

Here we are melting the cone and cylinder. So, sum of their volume will be equal to Volume of big cylinder.

For cylinder:

Radius of cylinder is 6 cm.

Height of cylinder is 10 cm.

For cone :

Radius of cone is 6 cm.

Height of cone is 5 cm.

Volume of cylinder = πr² h

Where, r and h are radius and height of cylinder.

Putting r and h in formula :

⟶π×(6)² ×10

⟶ 22/7 ×36×10

⟶ 7920/7

⟶ 1131.42

Volume of cylinder = 1131.42 cm³.

Volume of cone = 3/1 π r² h

Where, r and h are radius and height of cone.

Put r and h in formulas

⟶ 1³ × 22/7 ×(6)² ×5

⟶ 22/21 ×36×5

⟶ 3960/21

⟶ 188.57

Volume of cone is 188.57 cm³.

For big (new) cylinder :-

Diameter of cylinder is 8 cm

Radius = Diameter/2

Radius = 8/2 = 4

Radius of cylinder is 4 cm.

Let, h be the the height of cylinder.

Volume of big (new) cylinder = Volume of cylinder + volume of cone

⟶ 22/7 ×(4)² ×h = 1131.42+188.57

⟶ 22/7×16×h = 1319.99

⟶ 352/7 ×h = 1319.99

⟶ 352×h = 1319.99×7

⟶ 352×h = 9239.93

⟶ h = 3529339.93

⟶ h = 26.24

★ Therefore,

Height of big (new) cylinder is 26.24 (approx). Ans.