Question

rasheed got a playing top as his birthday present , which surprisingly had no colour on it. he wanted to colour it with his crayons.The top is shaped like a cone surmounted by a hemisphere . The entire top is 5cm in height and the diameter of the top is 3.5 cm . fin the area he has to colour . pie equals 22/7

Answer 1

Answer:

r =d/2

3.5/2=1.25

area =22/7×1.25×1.25×5=224. 55

Answer 2

Radius of hemisphere = Radius of cone

= $\sf{r=\frac{3.5}{2}cm=\frac{7}{4}cm}$

Height of cone, $\sf{h=5-r=(5-\frac{7}{4})cm=\frac{13}{4}cm}$

Slant height of cone,

= $\sf\red{l = \sqrt{ {r}^{2} + {h}^{2} }}$

= $\sf\red{\sqrt{ {( \frac{7}{4} )}^{2} + {( \frac{13}{4} )}^{2} } cm}$

= $\sf\red{ \frac{ \sqrt{49 + 169} }{4} cm}$

= $\sf\red{\frac{ \sqrt{218} }{4} cm}$

= $\sf\red{ \frac{14.765}{4} cm}$

= $\sf\red{3.691cm = 3.7cm(approx.)}$

TSA of the top to be coloured

= CSA of hemisphere + CSA of cone

= $\sf\red{2\pi {r}^{2} + \pi \: rl = \pi \: r(2r + l)}$

= $\sf\red{ \frac{22}{7} \times \frac{7}{4}(2 \times \frac{7}{4} + 3.7) {cm}^{2}}$

= $\sf\red{ \frac{11}{2} (3.5 + 3.7) {cm}^{2}}$

= $\sf\red{ \frac{11}{2} \times 7.2 {cm}^{2}}$

= $\sf\red{11 \times 3.6 {cm}^{2}}$

= $\sf\red{39.6 {cm}^{2}}$