Question

A balloon is in the form of a right circular cylinder of radius 1.5 m and height 4 m and is surmounted by hemisphere ends. If the radius is increased by 0.01 m and the height by 0.05 m, find the percentage change in the volume of the balloon

Answer 1

get ur percentage yourself

Answer 2

Answer:

2.4%

Step-by-step explanation:

A balloon is in the form of a right circular cylinder with hemisphere at it two ends

Height of cylinder = 4 m

Radius of cylinder = 1.5 m

Volume of cylinder = $\pi r^2 h$

                                = $3.14 \times 1.5^2 \times 4$

                                = $28.26 m^3$

radius of hemisphere = 1.5 m

Volume of hemisphere = $\frac{2}{3} \pi r^3$

Volume of 2 hemispheres = $2 \times \frac{2}{3} \pi r^3$

                                            = $2 \times \frac{2}{3}  \times 3.14 \times 1.5^3$

                                            = $14.13 m^3$

So, Volume of balloon = $28.26 m^3+14.13 m^3=42.39 m^3$

The radius is increased by 0.01 m and the height by 0.05 m

Radius = 1.5+0.01 = 1.51 m

Height = 4+0.05=4.05 m

Volume of cylinder = $\pi r^2 h$

                                = $3.14 \times 1.51^2 \times 4.05$

                                = $28.9960317 m^3$

radius of hemisphere = 1.51 m

Volume of hemisphere = $\frac{2}{3} \pi r^3$

Volume of 2 hemispheres = $2 \times \frac{2}{3} \pi r^3$

                                            = $2 \times \frac{2}{3}  \times 3.14 \times 1.51^3$

                                            = $14.4144881867 m^3$

Volume of new balloon = $28.9960317  m^3+14.4144881867 m^3=43.4105198867 m^3$

Change in Volume = 43.4105198867-42.39=1.0205198867 cubic m.

Percentage change = $\frac{Change}{Original} \times 100$

Percentage change = $\frac{1.0205198867}{42.39} \times 100$

Percentage change = $2.40745432107\%$

Hence the percentage change in the volume of the balloon is 2.4%