Question

If the base radius and height of a right circular cone are 3 cm and 4 cm in lengths, then the slant height is?
Please Also explain it ​

Answer 1

Step-by-step explanation:

we know that formula for finding slant height is

l^2=h^2+r^2

now the solution is

l^2=(4)^2+(3)^2

l^2= 16+9

l^2= 25

l= √25

l=5 cm

the slant height of cone is 5cm

Answer 2

Answer:

Diagram :

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{3\ cm}}\put(9.5,10){\sf{4\ cm}}\end{picture}$

• ✧ Radius = 3 cm
• ✧ Height = 4 cm

Here's the latex diagram of cone. See the answer from website Brainly.in for clear understanding.

Solution :

As per the provided information in the question, we have :

• ✧ Radius of cone = 3 cm.
• ✧ Height of cone= 4 cm.

We need to calculate the slant height of cone.

Here's the required formula to find the slant height of cone:

$\longrightarrow{\pmb{\sf{{\big( \: l \: \big)}^{2} = { \big( \: r \: \big)}^{2} + { \big( \: h \: \big)}^{2}}}}$

Where :

• ✧ l denotes slant height
• ✧ r denotes radius
• ✧ h denotes height

Substituting the given values in the formula to find slant height of cone :

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = { \big( \: r \: \big)}^{2} + { \big( \: h \: \big)}^{2}}}$

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = { \big( \: 3 \: \big)}^{2} + { \big( \: 4 \: \big)}^{2}}}$

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = { \big( \: 3 \times 3 \: \big)} + { \big( \: 4 \times 4 \: \big)}}}$

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = { \big( \: 9 \: \big)} + { \big( \: 16\: \big)}}}$

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = 9 + 16}}$

$\longrightarrow{\sf{{\big( \: l \: \big)}^{2} = 25}}$

$\longrightarrow{\sf{ l = \sqrt{25}}}$

$\longrightarrow{\sf{ l = \sqrt{5 \times 5}}}$

$\longrightarrow{\sf{\underline{\underline{\red{ l = 5 \: cm}}}}}$

Hence, the slant height of cone is 5 cm.

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Learn More :

Here's the some formulas related to cone. See the answer from website Brainly.in for clear understanding.

$\begin{gathered}\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}\end{gathered}$

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