Question

c. if cement costs $0.02/$\text{cm}^3$, what is the cost to fill the prism with ce

1. calculate the surface area and volume of the square pyramid shown belo

10 in
16 in
16 in

Explanation:

Step1: Calculate base area

$A_{base} = 16^2 = 256$ in$^2$

Step2: Calculate lateral triangle area

$A_{triangle} = \frac{1}{2} \times 16 \times 10 = 80$ in$^2$

Step3: Calculate total surface area

$SA = A_{base} + 4 \times A_{triangle} = 256 + 4 \times 80 = 256 + 320 = 576$ in$^2$

Step4: Find pyramid height first

Half the base side is $\frac{16}{2}=8$ in. Use Pythagoras: $h = \sqrt{10^2 - 8^2} = \sqrt{100-64} = \sqrt{36}=6$ in

Step5: Calculate pyramid volume

$V = \frac{1}{3} \times A_{base} \times h = \frac{1}{3} \times 256 \times 6 = 512$ in$^3$

Answer:

Surface Area: $576$ square inches
Volume: $512$ cubic inches