Question

A cylinder of same height and radius is placed on the top of a hemisphere. find the curved surface area of shape if the length of the shape be 7 cm.

Method required

Answer 1

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Answer 2

Hence the curved surface area is 231 $cm^2$.  

Step-by-step explanation:

Given:

Length of the shape = 7 cm

Let radius of the cylinder = r

and the height of the cylinder h = r                         [1]

Since cylinder is placed on the top of the hemisphere

So radius of hemisphere = radius of the cylinder = r

Now surface area of the cylinder = 2πrh + 2π$r^{2}$

                                                         = 2πr (r) + 2π  $r^{2}$       [from h = r]

                                                          = 2π $r^{2}$  + 2π $r^{2}$

                                                         = 4π $r^{2}$

Surface area of the cylinder = 2π $r^{2}$

Now total surface are of the shape = 4π $r^{2}$+ 2π $r^{2}$

                                                              = 6π $r^{2}$

Now total length of the shape = 7

⇒ Height of the cylinder + height of the hemisphere = 7

⇒ Height of the cylinder + radius of the hemisphere = 7  (height of the semisphere = radius of the hemisphere)

⇒ r+ r = 7

⇒ 2r = 7

⇒ $r= \frac{7}{2}$

Curved surface are of the shape = 6π$r^2$

                                                        = 6π $(\frac{7}{2})^2$

                                                        = 6π $\frac{49}{4}$

                                                        =  $6\times \frac{22}{7} \times\frac{49}{4}$    [π = $\frac{22}{7}$]

                                                        = $3\times 11 \times 7$

                                                        = $231 cm^2$

Hence the curved surface area is $231 cm^2$.