Question

Which is true about the volume or surface area of these prisms?

Answer 1

Let us find the Surface area and Volume of both Prisms A and B to conclude which is greater.

Consider Prism A :

$\bigstar$  Given Length of Prism A is 3 m

$\bigstar$  Given Width of Prism A is 2 m

$\bigstar$  Given Height of Prism A is 10 m

We know that :

$\bigstar$  Surface Area of a Rectangular Prism is given by : 2[lw + wh + lh]

$:\implies$  Surface area of Prism A : 2[(3)(2) + (2)(10) + (3)(10)]

$:\implies$  Surface area of Prism A : 2[6 + 20 + 30]

$:\implies$  Surface area of Prism A : 2[56]

$:\implies$  Surface area of Prism A : 112 m²

We know that :

$\bigstar$  Volume of a Rectangular Prism is given by : L x W x H

$:\implies$  Volume of Prism A : [3 x 2 x 10]

$:\implies$  Volume of Prism A : 60 m³

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Consider Prism B :

$\bigstar$  Given Length of Prism B is 2 m

$\bigstar$  Given Width of Prism B is 6 m

$\bigstar$  Given Height of Prism B is 5 m

We know that :

$\bigstar$  Surface Area of a Rectangular Prism is given by : 2[lw + wh + lh]

$:\implies$  Surface area of Prism B : 2[(2)(6) + (6)(5) + (2)(5)]

$:\implies$  Surface area of Prism B : 2[12 + 30 + 10]

$:\implies$  Surface area of Prism B : 2[52]

$:\implies$  Surface area of Prism B : 104 m²

We know that :

$\bigstar$  Volume of a Rectangular Prism is given by : L x W x H

$:\implies$  Volume of Prism B : [2 x 6 x 5]

$:\implies$  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.

$\bigstar$  Surface Area of Prism A is 112 m²

$\bigstar$  Surface Area of Prism B is 104 m²

Answer : Surface Area of Prism A  >  Surface Area of Prism B