Question

The number of volume of cylinder is half of its number of the total surface area. If the radius of its base is 7 cm , find the volume

Answer 1

Answer:

Ans:179.67

Step-by-step explanation:

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Answer 2

Answer:The volume of cylinder is 1437.34$cm^{3}$.

Step-by-step explanation:

Given:The number of volume of cylinder is half of its number of the total surface area. If the radius of its base is 7 cm.

To find:We have to find the volume of cylinder.

Explanation:

Step 1:We know that,

          Radius of cylinder(r) $= 7 cm$

           Volume of cylinder (V) $= \pi r^{2} h$

           Total surface area of cylinder $= 2\pi r (h+r)$

Step 2:It is given that the volume cylinder is half of its total surface area.

i.e.         $\frac{1}{2}$ × Volume of cylinder $=$ Total surface area of cylinder

⇒                                   $\frac{1}{2}$ × $\pi r^{2}h$ $= 2\pi r(h+r)$

⇒                                         $\frac{\pi r^{2} h}{\pi r} =$ $2[2(h+r)]$

⇒                                            $rh= 4(h+r)$

⇒                                            $rh= 4h+4r$

∵          $r=7cm$, so we have,

⇒                                            $7h=4h+4(7)$

⇒                                            $7h=4h+28$

⇒                                    $7h-4h=28$

⇒                                            $3h=28$

⇒                                              $h=\frac{28}{3}$

∴ Height of cylinder is $\frac{28}{3} cm$.

Step 3:As volume of cylinder is $\pi r^{2} h$.

i.e.      Volume of cylinder is $= \pi r^{2} h$

⇒                                           $=\frac{22}{7}(7)^{2}(\frac{28}{3})$

⇒                                           $=\frac{22}{7}$×$7$×$7$×$\frac{28}{3}$

⇒                                           $=22$×$7$×$9.34$

⇒                                           $=154$×$9.34$

⇒                                           $= 1437.34cm^{3}$

∴ The volume of cylinder is 1437.34$cm^{3}$.

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