Question

Can someone help me with this, Im so confused bru

Answer 1

Answer:

• The volumes of the figures are the same.

Step-by-step 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.

Answer 2

Answer:

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

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

The volumes of the figures are the same.

Step-by-step explanation:

Formulae

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

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

$\textsf{Area of a triangle}=\dfrac12 \times \sf base \times height$

$\textsf{Volume of a prism}=\sf base \: area \times height$

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

$\implies \textsf{Area of the triangular base}=\sf \dfrac{1}{2} \cdot 25 \cdot 2 \pi=25 \pi \:\:units^2$

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.