Question

10000000000000000000000000000000000000000000 Points

1) Find the curved and surface area and volume of the cone whose radius of base 21 cm and height 28cm?

Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

Given,

• Height of the cone = 28 cm
• Radius of Base = 21 cm

To Find,

• Curved surface area = ?
• Total surface area = ?
• Volume of the cone = ?

Find,

⇒Firstly we find the slant height of the cone .

∴Slant height of the cone( l ) = $\bold{\sqrt{r^{2} + h^{2} }}$

$\implies \bold{l = \sqrt{ 21^{2} + 28^{2} }}$

$\implies \bold{ l = \sqrt{ 441 + 784}}$

$\implies \bold{l = \sqrt{ 1225}}$

$\implies \boxed{\bold{ l = 35 \ cm }}$

Now Curved Surface Area :-

$\implies \boxed{\bold{ Curved \ Surface \ Area = \pi rl}}$

$\implies \bold{\frac{22}{7} \times 21 \times 35}$

$\implies \boxed{\bold{2310 \ cm^{2}}}$

Now Total Surface Area :-

$\implies \boxed{\bold{Total \ surface \ Area = \pi r(l + r})}$

$\implies \bold{\frac{22}{7} \times 21(35 + 21)}$

$\implies \bold{22 \times 3 \times 56 }$

$\implies \boxed{\bold{3696 \ cm^{2}}}$

Now Find the Volume of the Cone :-

$\implies \boxed{\bold{ Volume \ of \ the \ cone = \frac{1}{3} \times \pi r^{2} h}}$

$\implies \bold{\frac{1}{3} \times \frac{22}{7} \times 21 \times 21 \times 28}$

$\implies \bold{22 \times 3 \times 7 \times 28}$

$\implies \boxed{\bold{12936 \ cm^{3}}}$

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Answer 2

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Given:

• Height = 28 cm
• Radius of base = 21 cm

Need To Find:

• Curved surface area = ?
• Total surface area = ?
• Volume of the cone = ?

Explanation:

Firsty,

• Find the slant height of cone = ?

Therefore:

• Slant height of cone (l) = √r² + h²

Putting the values:

➠ L = √21² + 28²

➠ L = √441 + 784

➠ L = √1225

➠ L = 35 cm

• Hence, the slant height of cone(l) = 35 cm.

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In, Case 1:

• Find the curved surface area = ?

Formula used here:

• Curved surface area = πrl

Putting the values according to the given formula:

➠ 22/7 × 21 × 35

➠ 2310 cm²

• Hence, the curved surface area = 2310 cm².

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In Case 2:

• Find the total surface area = ?

Formula used here:

• Total surface area = πr(l + r)

Putting the values according to the given formula:

➠ 22/7 × 21(35 + 21)

➠ 22 × 3 × 56

➠ 3696 cm²

• Hence, total surface area = 3696 cm².

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In, Case 3:

• Find the volume of cone = ?

Formula used here:

• Volume of cone = 1/3 ×πr²h

Putting the values according to the given formula:

➠ 1/3 × 22/7 × 21 × 21 × 28

➠ 22 × 3 × 7 × 28

➠ 12936 cm³

• Hence, volume of the cone = 12936 cm³.

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