Question

5. Find the total surface of a cone which gas a radius if 8 cm
and a height of 12 cm.
(Hint: Surface area of a Cone)​

Answer 1

• Total surface area of cone is 563.2 cm² approximately.

Step-by-step explanation:

Given:-

• Radius of cone is 8 cm.
• Height of cone is 12 cm.

To find:-

• Total surface area of cone.

Solution:-

We know that,

Total surface area of cone = πrl + πr²

In which,

• r is Radius of cone.
• l is slant height of cone

r = 8 cm.

l = √r² + h²

l = √ 8 × 8 + 12 × 12

l = √64 + 144

l = √208

l = 14.4

l = 14.4 cm (approx)

Put r and l in formula :

=22/7 × 8 × 14.4 + 22/7 × 8 × 8

= 2534.4/7 + 1408/7

= 3942.4/7

= 563.2

Therefore,

Total surface area of cone is 563.2 cm² approximately.

________________________________

More formulas:-

• Surface area of a cuboid = 2 (lb + bh + hl)
• Surface area of a cube = 6a²
• Curved surface area of a cylinder = 2πrh
• Total surface area of a cylinder = 2πr(r+h)
• Curved surface area of a cone = πrl
• Total surface area of a right circular = πrl + πr²
• Surface area of a sphere =4πr²
• Curved surface area of a hemisphere = 2πr²
• Total surface area of a hemisphere = 3πr²
• Volume of a cube = a³
• Volume of a cylinder = πr²h
• Volume of a cone = 1/3πr²h
• Volume of a sphere =4/3πr²
• Volume of a hemisphere = 2/3πr²

Answer 2

$\frak{\pink{Given}}\begin{cases} \red{\textsf{Radius of cone= \textbf{8 cm}} }\\\orange{ \textsf{Height of cone = \textbf{12 cm }}}\end{cases}$

____________________...

$\sf\underline{\red{\:\:\:To \:Find:-\:\:\:}}$

$\bullet\:\textsf{Total Surface Area of cone = \textbf{?}}$

$\sf\underline{\red{\:\:\: Solution:-\:\:\:}}$

$\qquad \qquad\tiny \dag \: {\underline{\frak{Slant\: Height\:of\:cone\::}}}$

$:\implies \sf Slant \: Height = \sqrt{(Radius)^2 + (Height)^2}$

$:\implies \sf Slant \: Height = \sqrt{(8)^2 + (12)^2}$

$:\implies \sf Slant \: Height = \sqrt{64+ 144}$

$:\implies \sf Slant \: Height = \sqrt{208} \:cm$

$:\implies \underline{ \boxed{\sf Slant \: Height = 14.42\: cm}}$

______________________

$\qquad \qquad\tiny \dag \: {\underline{\frak{Total\: Surface\:Area\:of\:cone\::}}}$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = \pi rl + \pi r^{2}$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = \pi r (l + r)$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = \dfrac{22}{7} \times 8 (14.42 + 8)$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = \dfrac{22}{7} \times 8 \times 22.42$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = \dfrac{22}{7} \times 179.36$

$\dashrightarrow\:\:\sf Total \: Surface \: Area = 22 \times 25.62$

$\dashrightarrow\:\: \underline{ \boxed{\sf Total \: Surface \: Area = 563.64 \: {cm}^{2}}}$

$\therefore\:\underline{\textsf{Total Surface Area of cone is \textbf{563.64 cm ^{\text 2} }}}.$

_______________________

$\large\sf\underline{\red{\:\:\:Extra \: Shots:-\:\:\:}}$

$\boxed{\bigstar{\sf \ Cylinder :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cylinder= \pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ cylinder= 2\pi r h\\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ cylinder= 2\pi r (h+r)$

$\boxed{\bigstar{\sf \ Cone :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cone= \dfrac{1}{3}\pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Cone = \pi r l \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Cone = \pi r (l+r) \\ \\ \\ \sf {\textcircled{\footnotesize4}} Slant \ Height \ of \ cone (l)= \sqrt{r^2+h^2}$

$\boxed{\bigstar{\sf \ Hemisphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Hemisphere= \dfrac{2}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Hemisphere = 2 \pi r^2 \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Hemisphere = 3 \pi r^2$

$\boxed{\bigstar{\sf \ Sphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Sphere= \dfrac{4}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Surface\ Area \ of \ Sphere = 4 \pi r^2$