Hollow block

A hollow block is a prism with base dimensions a = b = 29 cm and height v = 15 cm. The wall thickness is 4.5 cm. What percentage of the block's volume is its cavity?

Final Answer:

p =  19.025 %

Step-by-step explanation:

$$\begin{gathered} a=29\text{cm} \\ b=a=29\text{cm} \\ c=15\text{cm} \\ h=4.5\text{cm} \\ {V}_1=a\cdot b\cdot c=29\cdot 29\cdot 15=12615{\text{cm}}^3 \\ A=a-2\cdot h=29-2\cdot 4.5=20\text{cm} \\ B=b-2\cdot h=29-2\cdot 4.5=20\text{cm} \\ C=c-2\cdot h=15-2\cdot 4.5=6\text{cm} \\ {V}_2=A\cdot B\cdot C=20\cdot 20\cdot 6=2400{\text{cm}}^3 \\ p=100\cdot \frac{V_2}{V_1}=100\cdot \frac{2400}{12615}=\frac{100\cdot 2400}{12615}=\frac{240000}{12615}=19.025\% \end{gathered}$$

Try another example