Question

3. What is the volume of this shape with a triangular hole through it? Show your answer to two decimal places Volume

Answer 1

To get the volume of that shape, which is a cylinder, with a triangular hole, we have to calculate the volume of the whole shape, then the volume of the triangle hole, and finally subtract the volume of the triangle hole from the total volume.

0. Calculating the volume of the cylinder.

The volume of the cylinder (Vc) is given by:

`V_c=\pi r^2\cdot l`

where r is the radius and l is the length.

In our problem, the radius id:

`r=(15)/(2)=7.5cm`

while l is 35cm. Replacing this data we get:

`V_c=\pi(7.5)^2^{}\cdot35`
`V_c=\pi\cdot56.26\cdot35`
`V_c=6185.01cm^3`

2. Calculating the volume of the triangle hole (triangle prism).

The volume of the triangle prism (Vt) is given by:

`V_t=(b\cdot h\cdot l)/(2)`

where b is the base (3cm), h is the height of the triangle (3), and l is the length (35cm). Replacing these values:

`V_t=(3\cdot3\cdot35)/(2)=157.5cm^3`

3. Subtracting Vt from Vc.

Finally, we have to subtract the volume to get the total volume (VT) without the hole:

`V_T=V_c-V_t=6185.01cm^3-157.5cm^3=6027.51cm^3`

Answer: 6027.51cm³