Question

of the prism below is a
square with a circular hole in it.
Work out the volume of the prism.
Give your answer to 3 s.f.
5 cm
6 cm
The cross-section
13 cm

Answer 1

Answer:

704 cm³

Step-by-step explanation:

Things to understand :

• The 3D figure removed by making a circular hole through the prism is a cylinder. The original shape was a rectangular prism.
• Volume of the prism is equal to the difference between the volume of the rectangular prism and cylinder.

Solving :

Volume (prism) = Volume (rectangular prism) - Volume (cylinder)

Volume = LWH - πr²h

Volume = 5 x 13 x 13 - π x 3² x 5

Volume = 845 - π x  45

Volume = 845 - 141.3

Volume = 704 cm³

Answer 2

$\boxed{\sf \: Answer : Volume \: of \: prism \: is \: 703.7 cm³}$

Step-by-step explanation:

Information about diagram- The diagram is a square prism with a circular hole in it.

Given:

length of prism (a) = 13cm

height of prism (h) = 5 cm

diameter of circle(d) = 6 cm

To find:

Volume of prism =?

Solution:

Formula that would be used,

$\sf volume \: of \: square \: prism = {a}^{2} h$

$\sf volume \: of \: cylinder = \pi {r}^{2} h$

Let's calculate the overall volume of prism,

Volume of prism(including volume of hole) V = a²h

$V = a²h \\ V = {13}^{2} \times 5 \\ V = 845 \: {cm}^{3}$

To find out the volume circular hole we need to find the radius of hole, since the diameter of hole is given we can calculate the radius by multiplying 1/2.

$r= \frac{d}{2} \\ r = \frac{6}{2} \\ r = 3 \: cm$

now calculate the volume of circular hole inside the prism,

Volume of circular hole(cylindrical shape) v= πr²h

$v = \pi {r}^{2} h \\ v = 3.14× {3}^{2} ×5 \\ v = 141.3 \: {cm}^{3}$

The volume of given diagram of prism (V') = Volume of overall prism(V) - volume of circular hole(v)

$V' = V- v \\ V' = 845 - 141.3 \: \\ V' = 703.7 \: {cm}^{3}$

Answer - Volume of prism is 703.7 cm³

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