Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius.
The total height of the toy is 15.5 cm. Find the total surface area of the toy

Answer 1

Answer:

We have,

Radius of cone = Radius of hemisphere = 3.5 cm.

Height of the toy = 15.5 cm

To calculate the CSA of cone we have to find first the Slant Height of the cone :]

Slant Height = h² + r²

Slant Height = (15.5)² + (3.5)²

Slant Height = 12.25 + 144

Slant Height = 156.25 cm²

Slant Height = 12.5 cm

Now, we will calculate the TSA of the toy :

➳ TSA of toy = CSA of hemisphere + CSA of cone

➳ TSA of toy = 2πr² + πrl

➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)

➳ TSA of toy = 24.5π + 43.75π

➳ TSA of toy = 68.25π

➳ TSA of toy = 68.25 * 22/7

➳ TSA of toy = 214.5 cm²

Answer 2

${\frak{Given}} \begin{cases} & \textsf{Radius of cone = 3.5 cm } \\ & \textsf{Height of cone = 15.5 cm} \end{cases}$

We have to find, Total surface area of toy.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Toy is hemispherical at bottom and conical at top.

⠀⠀⠀⠀⠀⠀⠀

$\setlength{\unitlength}{1cm}\begin{picture}(6, 4)\linethickness{0.26mm}\qbezier(5.8,2.0)(5.8,2.3728)(4.9799,2.6364)\qbezier(4.9799,2.6364)(4.1598,2.9)(3.0,2.9)\qbezier(3.0,2.9)(1.8402,2.9)(1.0201,2.6364)\qbezier(1.0201,2.6364)(0.2,2.3728)(0.2,2.0)\qbezier(0.2,2.0)(0.2,1.6272)(1.0201,1.3636)\qbezier(1.0201,1.3636)(1.8402,1.1)(3.0,1.1)\qbezier(3.0,1.1)(4.1598,1.1)(4.9799,1.3636)\qbezier(4.9799,1.3636)(5.8,1.6272)(5.8,2.0)\put(0.2,2){\line(1,0){5.6}}\put(3,2){\line(0,2){4.5}}\put(1.5,1.7){\sf{3.5 cm}}\qbezier(.2,2.05)(.7,3)(3,6.5)\qbezier(5.8,2.05)(5.3,3)(3,6.5)\put(2,4){\sf 12 cm}\put(3,2.02){\circle*{0.15}}\put(2.7,2){\dashbox{0.01}(.3,.3)}\qbezier(0.2,2)(2.9,-2)(5.8,2)\end{picture}$

⠀⠀⠀⠀⠀⠀⠀

Therefore

TSA of toy = CSA of hemisphere + CSA of cone

⠀⠀⠀⠀⠀⠀⠀

Slant height of cone, l = $\sf \sqrt{h^2 + r^2}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf l = \sqrt{3.5^2 + 12^2}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf l = \sqrt{12.25 + 144}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf l = \sqrt{156.25}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\pink{l = 12.5\;cm}}}}}\;\bigstar$

━━━━━━━━━━━━━━━━━━━━━

Therefore,

$\;\;\;\;\;\;\;\star\; 2 \pi r^2 + \pi rl$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 2 \pi (3.5)^2 + \pi (3.5)(12.5)$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 24.5 \pi + 43.75 \pi$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 68.25 \pi$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 68.25 \times \dfrac{22}{7}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\purple{l = 214 5\;cm}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀⠀

$\therefore$ Hence, Total surface area of toy is 214.5 cm².