Question

The volume of the pyramid shown in the figure is....cubic centimeters. If the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by.....cubic centimeters.
options;9,15,21,63

options;6,9,12,21

Answer 1

Answer:

Part a) The volume of the original pyramid is $15\ cm^{3}$

Part b) The volume of the pyramid increases by  $6\ cm^{3}$

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the base

h is the height of pyramid

see the attached figure to better understand the problem

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

$B=3^{2}=9\ cm^{2}$

$h=5\ cm$

substitute

$V=\frac{1}{3}(9)(5)=15\ cm^{3}$

Step 2

Find the volume of the new pyramid

$B=9\ cm^{2}$ -------> the area of the base is the same

$h=5+2=7\ cm$ ------> the height increase by $2\ cm$

substitute

$V=\frac{1}{3}(9)(7)=21\ cm^{3}$

Subtract the original volume from the new volume

$21\ cm^{3}-15\ cm^{3}=6\ cm^{3}$

Answer 2

Can't see the figure, but the basic way to solve this problem is to use the formula for volume of a pyramid which is (length * width * height )/3. Slant height is just the square root of ((length/2)2 + height2) recognizing that there is a right triangle there. Since slant height increased by 4 cm when its height increased by 2cm, you know that the length/2 term had to increase by the square root of 12 (22+root(12)2) = 42=16. From there you can figure out the rest pretty readily.