1 Find volume and surface area of the prism
Answers
Step-by-step explanation:
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.
Answer:
As the other answer suggests, if we don't place any restriction on what values the sides of a cuboid can take, there are way too many possibilities. We will assume the sides of the cuboid are all integers.
Given a cuboid of dimension a×b×c where a,b,c are integers, we have
AreaVol=2(ab+bc+ca)=abc
WOLOG, we will assume a≤b≤c and rewrite the formula for area as
(a+b)(a+c)=(ab+bc+ca)+a2=12Area+a2=120+a2
Since
Area=240⟹120=(ab+bc+ca)≥3a2⟹1≤a≤6
We have only 6 cases to analysis.
a=1a=2a=3a=4a=5a=6⟹120+a2=121=11×11⟹120+a2=124=4×31⟹120+a2=129=3×43⟹120+a2=136=23×17⟹120+a2=145=5×29⟹120+a2=156=22×3×13⇝⇝⇝⇝⇝⇝(a,b,c,Vol)=(1,10,10,100)(a,b,c,Vol)=(2,2,29,116)nothing(a,b,c,Vol)=(4,4,13,208)nothing(a,b,c,Vol)=(6,6,7,252)
To summarize, if the sides of the cuboids are all integers, there are 4 possible volumes