Question

Given figure is a solid composed of a cylinder with
hemisphere at one end. If the total surface area and the
height of the solid are 770 sq.cm and 14 cm respectively, find
the height of the cylinder.

Plz answer this with detailed explanation in copy......
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Answer 1

Answer:

Hope it helps you a lot......

Answer 2

Mensuration

Total surface area of the given solid$=770 \ cm^2$

Given height of solid $=14\ cm$

According to question,

$h+r=14$

$\implies r- 14-h$

CSA of cyllinderical part $= 2\pi rh= 2\times\frac{22}{7}\times (14-h)\times h$

CSA of hemispherical part $=2\pi r^2=2\times\frac{22}{7}\times(14-h)^2$

CSA of circular part  $= \pi r^2= \frac{22}{7}\times(14-h)^2$

Hence,

$2\pi rh+2\pi r^2+\pi r^2=770\\\\\implies 2\times\frac{22}{7}\times (14-h)\times h +2\times\frac{22}{7}\times(14-h)^2+ \frac{22}{7}\times(14-h)^2=770$

$\implies \frac{22}{7}(14-h)[ 2h+2(14-h)+14-h]=770\\\\\implies \frac{22}{7}(14-h)[2h+28-2h+14-h]=770\\ \\\implies \frac{22}{7}(14-h)(42-h)=770$

$\implies (14-h)(42-h)=\frac{770\times7}{22} \\\\\implies(14-h)(42-h)=245$

On solving this we get ,

$h =49 \ and \ h=7$

but 49 can't be the answer.

So 7 is the required height.