Let us find the Surface area and Volume of both Prisms A and B to conclude which is greater.
Consider Prism A :
[tex]\bigstar[/tex] Given Length of Prism A is 3 m
[tex]\bigstar[/tex] Given Width of Prism A is 2 m
[tex]\bigstar[/tex] Given Height of Prism A is 10 m
We know that :
[tex]\bigstar[/tex] Surface Area of a Rectangular Prism is given by : 2[lw + wh + lh]
[tex]:\implies[/tex] Surface area of Prism A : 2[(3)(2) + (2)(10) + (3)(10)]
[tex]:\implies[/tex] Surface area of Prism A : 2[6 + 20 + 30]
[tex]:\implies[/tex] Surface area of Prism A : 2[56]
[tex]:\implies[/tex] Surface area of Prism A : 112 m²
We know that :
[tex]\bigstar[/tex] Volume of a Rectangular Prism is given by : L x W x H
[tex]:\implies[/tex] Volume of Prism A : [3 x 2 x 10]
[tex]:\implies[/tex] Volume of Prism A : 60 m³
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Consider Prism B :
[tex]\bigstar[/tex] Given Length of Prism B is 2 m
[tex]\bigstar[/tex] Given Width of Prism B is 6 m
[tex]\bigstar[/tex] Given Height of Prism B is 5 m
We know that :
[tex]\bigstar[/tex] Surface Area of a Rectangular Prism is given by : 2[lw + wh + lh]
[tex]:\implies[/tex] Surface area of Prism B : 2[(2)(6) + (6)(5) + (2)(5)]
[tex]:\implies[/tex] Surface area of Prism B : 2[12 + 30 + 10]
[tex]:\implies[/tex] Surface area of Prism B : 2[52]
[tex]:\implies[/tex] Surface area of Prism B : 104 m²
We know that :
[tex]\bigstar[/tex] Volume of a Rectangular Prism is given by : L x W x H
[tex]:\implies[/tex] Volume of Prism B : [2 x 6 x 5]
[tex]:\implies[/tex] Volume of Prism B : 60 m³
We can notice that Volumes of both Prism A and B are Equal, But the Surface Areas are not.
[tex]\bigstar[/tex] Surface Area of Prism A is 112 m²
[tex]\bigstar[/tex] Surface Area of Prism B is 104 m²
Answer : Surface Area of Prism A > Surface Area of Prism B
