Question

A toy is in the shape of a cone surmounted by a hemisphere as shown in the
following figure. The radius of each cone and the hemisphere is 5cm and the total
height of the toy 17cm. Find the total surface area of the toy.

Answer 1

Answer:

TSA of the TOY

CSA of CONE+SA of Hemisphere

πrl +2 πr 2

h = 12,r=5, I=v5^2+12^2 =v169=13cm

πrl+2πr^2 = π x 5x13 +2xπx5^2

= 65π+50π =115π =361. I cm2

TSA of the TOY=36l. I cm2

Answer 2

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Step-by-step explanation:

Radius of cone = Radius of hemisphere = 5cm

Height of conical part = Height of the toy - Radius of hemisphere.

= 17 - 5

= 12cm.

Now, surface of hemisphere part

$\: \: \: \: \: \: \: \: \: \: \: \: = {2\pi \: r}^{2} = 2\pi. {5}^{2} \\ = 50\pi \: sq.cm.$

$and \: Curved \: surface \: of \: conical \: part \: = \pi \: rl$

$\: \: \: \: = \pi.5. \sqrt{ {12}^{2} + {5}^{2} } , ❴ \: ∵ \: \: {l}^{2} = \sqrt{ {h}^{2} + {r}^{2} } ❵$

$\: \: \: \: = \pi.5. \sqrt{144 + 25}$

$\: \: \: \: = \pi.5 \sqrt{169} = \pi.5.13$

$\: \: \: \: = 65\pi \: sq. \: cm.$

$∴ \: \: Total \: surface \: of \: the \: toy \: = 50\pi + 65\pi \\ = 115\pi \: sq.cm$