Neha got a playing top as her birthday present, which surprisingly had no colour on it.He wanted to colour it with her crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top Is 3.5cm.find the area he has to colour
Answers
Answer:
it's 5 cm
Step-by-step explanation:
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Step-by-step explanation:
Radius of hemisphere = Radius of cone
= \sf{r=\frac{3.5}{2}cm=\frac{7}{4}cm}r=
2
3.5
cm=
4
7
cm
Height of cone, \sf{h=5-r=(5-\frac{7}{4})cm=\frac{13}{4}cm}h=5−r=(5−
4
7
)cm=
4
13
cm
Slant height of cone,
= \sf\red{l = \sqrt{ {r}^{2} + {h}^{2} }} l=
r
2
+h
2
= \sf\red{\sqrt{ {( \frac{7}{4} )}^{2} + {( \frac{13}{4} )}^{2} } cm}
(
4
7
)
2
+(
4
13
)
2
cm
= \sf\red{ \frac{ \sqrt{49 + 169} }{4} cm}
4
49+169
cm
= \sf\red{\frac{ \sqrt{218} }{4} cm}
4
218
cm
= \sf\red{ \frac{14.765}{4} cm}
4
14.765
cm
= \sf\red{3.691cm = 3.7cm(approx.)}3.691cm=3.7cm(approx.)
TSA of the top to be coloured
= CSA of hemisphere + CSA of cone
= \sf\red{2\pi {r}^{2} + \pi \: rl = \pi \: r(2r + l)}2πr
2
+πrl=πr(2r+l)
= \sf\red{ \frac{22}{7} \times \frac{7}{4}(2 \times \frac{7}{4} + 3.7) {cm}^{2}}
7
22
×
4
7
(2×
4
7
+3.7)cm
2
= \sf\red{ \frac{11}{2} (3.5 + 3.7) {cm}^{2}}
2
11
(3.5+3.7)cm
2
= \sf\red{ \frac{11}{2} \times 7.2 {cm}^{2}}
2
11
×7.2cm
2
= \sf\red{11 \times 3.6 {cm}^{2}} 11×3.6cm
2
= \sf\red{39.6 {cm}^{2}} 39.6cm
2