Question

Consider a pyramid with a square base side of $6$ inches and with a height of $12$ inches, as shown below. If we cut off the top of the pyramid parallel to the base $3$ inches from the tip, what is the volume of the remaining solid?

• A. $141.75$
• B. $140$
• C. $135.48$
• D. $144$
• E. $130$

Answer 1

The correct option is A $141.75$

a pyramid of a square base side of 6 inches.

height = $12$ inches

for smaller pyramid given :-

height = $3$ inches

Base square of side = $1.5$ inches

volume of larger pyramid = $\frac{1}{3}$ Base area $\times$ height

$=\frac{1}{3}(6{)}^2\times 12$

$=36\times 4=144inc{h}^3$

Volume of smaller pyramid $=\frac{1}{3}$ Base area $\times$ height

$=\frac{1}{3}(1.5{)}^2\times 3$

$=(1.5{)}^2=2.25inc{h}^3$

So, volume of remaining solid

= larger volume - smaller volume

$=144-2.25$

$=141.75inc{h}^3$