Question

The height of a cone is 16 cm and base radius is 12 cm. Find the curved surface area and the total surface area of the cone.(use π = 3.14)​

Answer 1

Answer:

$\setlength{\unitlength}{1cm}\begin{picture}(6, 4)\linethickness{0.26mm}</p><p>\qbezier(5.8,2.0)(5.8,2.3728)(4.9799,2.6364)\qbezier(4.9799,2.6364)(4.1598,2.9)(3.0,2.9)\qbezier(3.0,2.9)(1.8402,2.9)(1.0201,2.6364)\qbezier(1.0201,2.6364)(0.2,2.3728)(0.2,2.0)\qbezier(0.2,2.0)(0.2,1.6272)(1.0201,1.3636)\qbezier(1.0201,1.3636)(1.8402,1.1)(3.0,1.1)\qbezier(3.0,1.1)(4.1598,1.1)(4.9799,1.3636)\qbezier(4.9799,1.3636)(5.8,1.6272)(5.8,2.0)\put(0.2,2){\line(1,0){2.8}}\put(3.2,4){\sf{16 cm}}\put(3,2){\line(0,2){4.5}}\put(1.4,1.6){\sf{12 cm}}\qbezier(.185,2.05)(.7,3)(3,6.5)\qbezier(5.8,2.05)(5.3,3)(3,6.5)\put(3,2.02){\circle*{0.15}}\put(2.7,2){\dashbox{0.01}(.3,.3)}\end{picture}$

• Slant Height of the Cone :

$\dashrightarrow\sf l^2=h^2+r^2\\\\\\\dashrightarrow\sf l^2=(16)^2+(12)^2\\\\\\\dashrightarrow\sf l^2=256+144\\\\\\\dashrightarrow\sf l^2=400\\\\\\\dashrightarrow\sf l = \sqrt{400} \\\\\\\dashrightarrow\sf l = 20 \:cm$

$\rule{150}{1.2}$

• Curved Surface Area of Cone :

$:\implies\sf CSA=\pi rl\\\\\\:\implies\sf CSA=3.14 \times 12\:cm \times 20\:cm\\\\\\:\implies\underline{\boxed{\sf CSA=753.6\:cm^2}}$

⠀⠀⠀⠀$\rule{150}{2}$

• Total Surface Area of Cone :

$:\implies\sf TSA=\pi r(l+r)\\\\\\:\implies\sf TSA=3.14 \times 12\:cm \times (20\:cm+12\:cm)\\\\\\:\implies\sf TSA=3.14 \times 12\:cm \times 32\:cm\\\\\\:\implies\underline{\boxed{\sf TSA=1205.76\:cm^2}}$