there is a cylinder of heighthe 30 cm and its radius is 14 cm .it is meled to form a new cylinder of radius 7 cmfind height of new cylinder
Answers
Answer:
Height of old cylinder, h = 30 cm
Radius of old cylinder, r = 14 cm
Radius of new cylinder, R = 7 cm
⠀⠀⠀
Need to find:
Height of new cylinder?
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━
☯ Let Height of new cylinder be H cm.
⠀⠀⠀
\begin{gathered}\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \: Question :}}}}}\mid}\\\\\end{gathered}
∣
★AccordingtoQuestion:
∣
★ Volume of old cylinder = Volume of new Cylinder
⠀
\begin{gathered}:\implies\sf \pi r^2 h = \pi R^2 H\\ \\\end{gathered}
:⟹πr
2
h=πR
2
H
\begin{gathered}:\implies\sf \cancel{ \dfrac{22}{7}} \times (14)^2 \times 30 = \cancel{ \dfrac{22}{7}} \times (7)^2 \times H\\ \\\end{gathered}
:⟹
7
22
×(14)
2
×30=
7
22
×(7)
2
×H
\begin{gathered}:\implies\sf 14 \times 14 \times 30 = 7 \times 7 \times H\\ \\\end{gathered}
:⟹14×14×30=7×7×H
\begin{gathered}:\implies\sf H = \dfrac{\cancel{14} \times \cancel{14} \times 30}{\cancel{7} \times \cancel{7}}\\ \\\end{gathered}
:⟹H=
7
×
7
14
×
14
×30
\begin{gathered}:\implies\sf H = 2 \times 2 \times 30\\ \\\end{gathered}
:⟹H=2×2×30
\begin{gathered}:\implies{\boxed{\frak{\pink{H = 120\;cm}}}}\;\bigstar\\ \\\end{gathered}
:⟹
H=120cm
★
\therefore\;{\underline{\sf{Hence,\; Height\;of\;new\;cylinder\;is\; \bf{120\;cm}.}}}∴
Hence,Heightofnewcylinderis120cm.
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━
\begin{gathered}\qquad\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: More\:to\:Know :}}}}}\mid}\\\\\end{gathered}
∣
★MoretoKnow:
∣
CSA of Cylinder = \sf 2 \pi rh2πrh
⠀
TSA of Cylinder = \sf 2 \pi r(h + r)2πr(h+r)
⠀
Volume of Cylinder = \sf \pi r^2 hπr
2
h
Step-by-step explanation:
I think it will help u