Question

Find the lateral area of this cone.

Answer 1

Step-by-step explanation:

lateral surface area here = πrl

r = 10

l = √h²+r²= √ 24²+ 10² = 26

lateral surface area = 10 × 26 × π

= 260π in²

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Answer 2

Answer:

The lateral area of cone is 260π in².

Step-by-step explanation:

Given :

• $\small\blue\bull$ Height of cone = 24 in.
• $\small\blue\bull$ Radius of cone = 10 in.

$\begin{gathered}\end{gathered}$

To Find :

• $\small\blue\bull$ Slant height of cone
• $\small\blue\bull$ Lateral surface area of cone

$\begin{gathered}\end{gathered}$

Using Formulas :

$\star{\underline{\boxed{\sf{\purple{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}}}$

• $\pink\star$ l = slant height
• $\pink\star$ r = radius
• $\pink\star$ h = height

$\star{\underline{\boxed{\sf{\purple{La_{(Cone)}= \pi r\ell}}}}}$

• $\pink\star$ La = Lateral area
• $\pink\star$ π = 3.14
• $\pink\star$ r = radius
• $\pink\star$ l = slant height

$\begin{gathered}\end{gathered}$

Solution :

Finding the slant height of cone by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10)}^{2} + {(24)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10 \times 10)} + {(24 \times 24)}}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{(100)+(576)}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{100 + 576}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{676}}}}\\\\\quad{\longrightarrow{\sf{\ell = 26 \: in}}}\\\\\quad\star\underline{\boxed{\sf{\pink{\ell = 26 \: in}}}} \end{gathered}$

Hence, the slant height of cone is 26 in.

$\begin{gathered}\end{gathered}$

Now, finding the lateral area of cone by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{La_{(Cone)} = \pi r \ell}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 10 \times 26}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 260}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = 260\pi\: {in}^{2}}}}\\\\ \qquad{\star{\underline{\boxed{\sf{\pink{La_{(Cone)} = 260\pi \: {in}^{2}}}}}}}\end{gathered}$

Therefore, the lateral area of cone is 260π in².

$\rule{300}{2.5}$