Question

A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively. Determine the surface area of the toy.
(use π = 3.14)

Answer 1

Answer:

103.62 cm²

Step-by-step explanation:

Given, height of cone = 4 cm and diameter = 6 cm. Then, radius = 3 cm.

Slant height(l) = √r² + h²

                       = √3² + 4²

                       = 5 cm.

∴ Surface area of cone = πrl

                                      = 3.14 * 3 * 5

                                     = 47.1 cm²

∴ Surface area of hemisphere = 2πr²

                                                  = 2 * 3.14 * (3)²

                                                  = 56.52 cm²

Total surface area of toy = Area of cone + Area of hemisphere

                                         = 47.1 + 56.52

                                         = 103.62 cm²

Hope it helps!

Answer 2

Given,

Diameter = 6 cm
Radius = 6/2 cm = 3 cm
Height = 4 cm

T.S.A of Toy = T.S.A of Cone + T.S.A of hemisphere.

At first we will find the C.S.A of Cone then C.S.A of Hemisphere.

Now,

C.S.A of Cone

$= > c.s.a = \pi \: r \: l$

Hence, Slant Height (l) is not given then we will find.

$= > {l}^{2} = {h}^{2} + {r}^{2}$

$= > {l}^{2} = {4}^{2} + {3}^{2}$

$= > {l}^{2} = 25$

$= > \: l \: = \sqrt{25}$

$= > \: l \: = 5 \: cm$

As per Formula,

$= > c.s.a = \pi \: r \: l$

$= > c.s.a = 3.14 \times 3 \times 5$

$= > c.s.a = 47.1 \: {cm}^{2}$

Now,

T.S.A of Hemisphere

$= > t.s.a = 2 \times \pi \times {r}^{2}$

$= > t.s.a = 2 \times 3.14 \times 3 \times 3$

$= > t.s.a = 56.52 \: {cm}^{2}$

Now, T.S.A of toy = (47.1+56.52) cm^2

=> T.S.A of Toy = 103.62 cm^2


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