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?*

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

Answer 1

★ 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 ✔ ✰

______________________________

Answer 2

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.

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

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