Question

1)
(c) Volume of a cylinder is 2,376 cm . If the diameter of its base is 12 cm, then find
its height.
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Answer 1

Given -

• Volume of cylinder = 2376cm³

• Base Diameter = 12cm

To find -

• Cylinder's height

Formula used -

• Volume of cylinder.

Solution -

In the question, we are provided with the volume and base diameter of a cylinder, and we need to finding it's height. Now, First we will, name the height as h, then We will find the radius of the cylinder, then we will use the formula of volume of cylinder, and Hence, the height of cylinder will be obtained to us. Let's do it!

So -

First we will convert Diameter into radius, by dividing, the given Diameter by 2, as radius is half of diameter.

Radius = $\tt\cancel\dfrac{12}{2}$

Radius = 6cm

So the radius is 6cm

Now -

We will find the height, by using the formula of volume of volume of cylinder.

$\tt Volume_{(cylinder)}$ = πr²h

Where -

π = $\tt\dfrac{22}{7}$

r = Radius

h = Height

On substituting the values -

$\tt 2376 = \dfrac{22}{7} \times {(6cm)}^{2} \times\ h \\ \\ \\ \tt 2376 = \dfrac{22}{7} \times 36cm \times h \\ \\ \\ \tt\ h = \tt\dfrac{2376 \times 7}{22 \times 36} \\ \\ \\ \tt h = \dfrac{16632}{792} \\ \\ \\ \tt h = 21cm$

$\therefore$ The height of the cylinder is 21 cm

Verification -

Volume = πr²h

2376cm³ = $\tt\dfrac{22}{7}$ × 36cm × 21cm

2376cm³ = 22 × 36cm × 3cm

2376cm³ = 2376cm³

Hence, verified!

More formulae -

1. Curved surface area = 2πrh

2. Total surface area = 2πr(r + h)

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Answer 2

Answer:

Given :-

• Volume of a cylinder is 2376 cm. The diameter of its base is 12 cm.

To Find :-

• What is the height of a cylinder.

Formula Used :-

★ Volume of cylinder = πr²h ★

Solution :-

Given :

• Volume of a cylinder = 2376 cm
• Diameter of its base = 12 cm

First we have to find the radius,

We know that,

✰ Radius = Diameter ÷ 2 ✰

↦ Radius = 12 ÷ 2

➦ Radius = 6 cm

Now we have to find the height of the cylinder,

According to the question by using the formula we get,

⇒ 22/7 × (6)² × h = 2376

⇒ 22/7 × 36 × h = 2376

⇒ h = 2376 × 7/36 × 22

⇒ h = 16632/792

➠ h = 21 cm

∴ The height of the cylinder is 21 cm .

★ Let's Verify ★

⇒ 22/7 × (6)² × h = 2376

Put h = 21 we get,

⇒ 22/7 × 36 × 21 = 2376

⇒ 22/7 × 756 = 2376

⇒ 2376 = 2376

➦ LHS = RHS

Hence, Verified ✔