Question

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

Answer 1

Solution:-

Since The total height of the Toy is 15.5cm & Radius of Hemisphere is 3.5cm.

=> Height of Cone = 12 cm.

TOTAL SURFACE AREA OF THE TOY = Surface Area of Cone + Surface Area of Hemisphere.

=> Surface Area of Cone = πrl

For l,

l = √ h² + r²

=> l = √ 144 + 12.25

=> l = √ 156.25 = 12.5 cm.

=> Surface Area of Cone = 22/7 * 3.5 * 12.5

=>$\boxed{Surface Area of Cone= 137.5 cm}$

& Surface Area of Hemisphere = 2πr²

=> 2 * 22/7 * 3.5²

=> 77cm²

Hence,

Total Surface Area of the Toy = 77 + 137.5

=> Total Surface Area of the Toy= 214.5 cm².

Answer 2

$\mathfrak{\huge{Answer:}}$

$\mathbb{GIVEN}$

Radius of the cone = Radius of the hemisphere = 3.5 cm

Total length of the toy = 15.5 cm

$\mathbb{TO\:FIND}$

The Total Surface Area of the toy

$\mathbb{METHOD}$

We know that:-

$\sf{Curved\:Surface\:Area\:of\:cone = \pi r l}$

Length of the cone = $\sf{\sqrt{h^{2} + r^{2}}}$

Length of the cone = 12.5 cm

=》 Curved Surface Area of the cone = $\sf{\pi \times 3.5 \times 12.5}$

=》 Curved Surface Area of the cone = $\boxed{\tt{137.5\:cm^{2}}}$

We also know that:-

$\sf{Curved\:Surface\:Area\:of\:hemisphere = 2 \pi r^{2}}$

=》 Curved Surface Area of the hemisphere = $\sf{2 \pi \times 3.5^{2}}$

=》 Curved Surface Area of the hemisphere = $\boxed{\tt{77\:cm^{2}}}$

Total Surface Area of the toy = $\tt{ 137.5 + 77\:cm^{2}}$

Thus, answer will be $\mathfrak{\huge{214.5\:cm^{2}}}$