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tamaranim1 [39]
3 years ago
8

The volume of the pyramid shown in the figure is cubic centimeters. If the slant height of the pyramid increases by 4 centimeter

s and its height increases by 2 centimeters, the volume of the pyramid increases by cubic centimeters.

Mathematics
1 answer:
Nostrana [21]3 years ago
5 0

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:

<u><em>The complete question is</em></u>

Part 1) The volume of the pyramid shown in the figure is 9,15,21, or 63 cubic centimeters?. Part 2) 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 6,9,12 or 21 cubic centimeters?

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

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}

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