Question

Which pyramid has a greater volume, and how much greater is its volume? A rectangular pyramid on the left with a base of 7 inches by 6 inches and height of 3 inches. A rectangular pyramid on the right with a base of 4 inches by 3 inches and a height of 10 inches.

Answer 1

Answer:

Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of $42in^3$

How much greater is its volume? its volume is $2in^3$ greater than the second (right) pyramid

Step-by-step explanation:

Equation to find the volume of a pyramid:

$V=\frac{A_bh}{3}$

where $A_b$ is the area of the base, and $h$ is the height.

• First pyramid:

length: $l=7in$

width: $w=6in$

height: $h=3in$

Area of the rectangular base:

$A_b=lw\\A_b=7in*6in\\A_b=42in^2$

Volume of the first pyramid:

$V_1=\frac{A_bh}{3}\\ \\V_1=\frac{42in^2*3in}{3} \\\\V_1=\frac{126in^3}{3} \\\\V_1=42in^3$

• Second pyramid:

length: $l=4in$

width: $w=3in$

height: $h=10in$

Area of the rectangular base:

$A_b=lw\\A_b=4in*3in\\A_b=12in^2$

Volume of the second pyramid:

$V_2=\frac{A_bh}{3} \\\\V_2=\frac{12in^2*10in}{3}\\ \\V_2=\frac{120in^3}{3} \\\\V_2=40in^3$

Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of $42in^3$

How much greater is its volume? its volume is $2in^3$ greater than the second (right) pyramid