Question

Please I need help. I don’t understand this.

Answer 1

Answer: πr2h

= π×282×34

= 26656π

= 83742.29377409 centimeters3

Explanation:

Answer 2

The volume of the composite figure is 12,719 cm³ to the nearest whole number.

Explanation:

The composite figure is composed of a cone and a half-sphere.

To calculate the volume of the figure, sum the volume of the cone and the volume of the half-sphere.

`\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=(1)/(3) \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`
`\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=(2)/(3) \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}`

Therefore, the equation for the volume of the composite figure is:

`V=(1)/(3) \pi r^2 h+(2)/(3) \pi r^3`

From inspection of the given diagram:

• d = 28 cm
• h = 34 cm
• π ≈ 3.14

As the diameter of a circle is twice its radius, r = 14 cm.

Substitute the values of r, h and π into the equation and solve for V:

`\begin{aligned}\implies V&=(1)/(3) \pi r^2 h+(2)/(3) \pi r^3\\\\&=(1)/(3) (3.14) (14)^2 (34)+(2)/(3) (3.14) (14)^3\\\\&=(1)/(3) (3.14) (196) (34)+(2)/(3) (3.14) (2744)\\\\&=6974.98666...+5744.10666...\\\\&=12719.09333...\\\\&=12719\;\sf cm^3\;\;(nearest\;whole\;number)\end{aligned}`

Therefore, the volume of the composite figure is 12,719 cm³ to the nearest whole number.