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

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.

Answer 2

Part a) The volume of the original pyramid is
`15\ cm^(3)`

Part b) The volume of the pyramid increases by
`6\ cm^(3)`

Explanation:

we know that

The volume of the pyramid is equal to

`V=(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=(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=(1)/(3)(9)(7)=21\ cm^(3)`

Subtract the original volume from the new volume

`21\ cm^(3)-15\ cm^(3)=6\ cm^(3)`