Answer:
Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of [tex]42in^3[/tex]
How much greater is its volume? its volume is [tex]2in^3[/tex] greater than the second (right) pyramid
Step-by-step explanation:
Equation to find the volume of a pyramid:
[tex]V=\frac{A_bh}{3}[/tex]
where [tex]A_b[/tex] is the area of the base, and [tex]h[/tex] is the height.
length: [tex]l=7in[/tex]
width: [tex]w=6in[/tex]
height: [tex]h=3in[/tex]
Area of the rectangular base:
[tex]A_b=lw\\A_b=7in*6in\\A_b=42in^2[/tex]
Volume of the first pyramid:
[tex]V_1=\frac{A_bh}{3}\\ \\V_1=\frac{42in^2*3in}{3} \\\\V_1=\frac{126in^3}{3} \\\\V_1=42in^3[/tex]
length: [tex]l=4in[/tex]
width: [tex]w=3in[/tex]
height: [tex]h=10in[/tex]
Area of the rectangular base:
[tex]A_b=lw\\A_b=4in*3in\\A_b=12in^2[/tex]
Volume of the second pyramid:
[tex]V_2=\frac{A_bh}{3} \\\\V_2=\frac{12in^2*10in}{3}\\ \\V_2=\frac{120in^3}{3} \\\\V_2=40in^3[/tex]
Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of [tex]42in^3[/tex]
How much greater is its volume? its volume is [tex]2in^3[/tex] greater than the second (right) pyramid
