Question

Can someone help me with this, Im so confused bru

Answer 1

`\sf Cylinder: \quad V=225 \pi \:\:units^3`

`\sf Prism: \quad V=225 \pi \:\:units^3`

The volumes of the figures are the same.

Explanation:

Formulae

`\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

`\textsf{Radius of a circle}=(1)/(2)d \quad \textsf{(where d is the diameter)}`

`\textsf{Area of a triangle}=\frac12 * \sf base * height`

`\textsf{Volume of a prism}=\sf base \: area * height`

Volume of the cylinder

Given:

• d = 10 ⇒ r = 5
• h = 9

Substitute the given values into the formula and solve for V:

`\implies \sf V=\pi \cdot 5^2 \cdot 9`

`\implies \sf V=\pi \cdot 25 \cdot 9`

`\implies \sf V=225 \pi \:\:units^3`

Volume of the triangular prism

Given values of triangular base:

• base = 25
• height = 2π

`\implies \textsf{Area of the triangular base}=\sf (1)/(2) \cdot 25 \cdot 2 \pi=25 \pi \:\:units^2`

Given values of prism:

• Area of base = 25π
• Height = 9

Substitute the given values into the formula and solve for V:

`\implies \sf V=25 \pi \cdot 9`

`\implies \sf V=225 \pi \:\:units^3`

Conclusion

The volumes of the figures are the same.

Answer 2

• The volumes of the figures are the same.

Explanation:

Let's find the volume of each figure and compare.

Volume of cylinder

Use equation:

• V = πr²h

Substitute values and find the volume:

• V = π*(10/2)²*9 = 225π unis³

Volume of prism

Use equation:

• V = Bh

Since the base is the right triangle, its area is:

• B = ab/2 = 2π*25/2 = 25π

Find the volume:

• V = 25π*9 = 225π unis³

Compare

• We see both volumes are equal, so the answer is the same.