Math, asked by pritamkanhed21, 3 months ago

*If the volume of an cylinder is 700 cubic centimeters and the area of the base is 100 square centimeters, what is the length of the cylinder?*

1️⃣ 70 cm
2️⃣ 7 cm
3️⃣ 700 cm
4️⃣ 7 sqcm​

Answers

Answered by BrainlyVanquisher
21

★ Appropriate Question :

  • If the volume of an cylinder is 700 cubic centimeters and the area of the base is 100 square centimeters, what is the length of the cylinder?*

  • 1). 70 cm
  • 2). 7 cm ✔
  • 3). 700 cm
  • 4). 7 sqcm

★ Required Solution :

★ Values given to us :

  • ➻ Volume of cylinder = 700cm³

  • ➻ Area of base of cylinder = 100cm²

★ Formula used here :

  • ➻ area of base of cylinder = πr²

  • ➻ Volume of cylinder = πr²h

✴ Let ‘h’ be length of cylinder

★ According to question :

  • ➻ Volume of cylinder = area of base of cylinder

  • ➻ 700cm³ = 100h

  • ➻ 700 / 100 = ‘h’

  • ★ value of height = 7 cm ★

✴ Therefore :

✰ Option (2) is correct ✔ ✰

______________________________

Answered by SƬᏗᏒᏇᏗƦƦᎥᎧƦ
84

Information provided with us :

  • The volume of an cylinder is 700 cubic centimeters.
  • The area of the base is 100 square centimeters.

What we have to calculate :

  • Length of the cylinder?

Performing Calculations :

Here we have to calculate the length of the cylinder i.e., height of cylinder.

  • V = 700cm³
  • A = 100cm²

We would be using the formulas of calculating the volume of cylinder and area of cylinder.

  • \boxed{\bf{Area \: of \:  cylinder \:  =  \: \pi \: r }^{2}}  \:   \pink\bigstar

: \: \implies \: \sf{Area \: of \:  cylinder \:  =   \: 100cm}^{3}  \: (given \: in \: question)

★ Now, volume of cylinder :

  • \boxed{\bf{Volume \:  of  \: cylinder \:  =  \: \pi \: r }^{2}h}  \:   \pink\bigstar

Where,

  • r is radius
  • h is height
  • Value of π is 22/7

We're given with the value of volume of cylinder as 700cm³ and the value of (πr²) is 100 cm³ so we would substitute them in this formula.

:  \: \implies \: \sf{700 \:  =  \: \pi \: r }^{2}h \\  \\ :  \: \implies \: \sf{700 \:  =  \:100h} \\  \\ :  \: \implies \: \sf{700 \:  =  \:100 \times h}  \\  \\ :  \: \implies \: \sf{ h \:  =  \:  \frac{700}{100} } \\  \\ :  \: \implies \: \sf{ h \:  =  \:   \cancel\frac{700}{100} } \\  \\ :  \: \implies \: \sf{ h \:  =  \:  \frac{70}{10} } \\  \\ :  \: \implies \: \sf{ h \:  =  \:   \cancel\frac{70}{10} } \\  \\ :  \: \implies \: \sf{ h \:  =  \:  \frac{7}{1} } \\  \\ :  \: \implies \:  \red{\bf{ h \:  =  \:  7} }

 \bf{\underline{{\therefore \: Length \: of \: the \: cylinder \: is \: 7cm}}}

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