Question

the first box measures 18 inches by 8 inches by 15 inches. the second box is 10 inches tall and the area of the base measures 196 inches square which box has a greater volume and by how much?

Answer 1

`\bold{\huge{\underline{ Solution }}}`

Given :-

• We have given two boxes
• The dimensions of the first box is 18 inches ,8 inches and 15 inches
• The height of the second box is 10 inches whereas it's base area is 196 inches²

To Find :-

• We have to compare the volume of both the boxes and then we have to tell which box has a greater volume and by how much ?

Procedure to Solve :-

Firstly, we will find the volume of both the boxes then we will compare the volume of both the boxes. Then, we will subtract the lesser volume with greater volume and hence, we got the answer.

Let's Begin :-

According to the question :-

• We have two boxes that is first box and second box.
• We have the dimensions of both the boxes that is ( 18 × 8 × 15 ) and ( 10 × 196 ) .
• From the dimensions, we can conclude that :-
• The given boxes are in the shape of cuboid.

We know that,

Volume of cuboid

`\bold{\pink{ = Length }}{\bold{\pink{*{Breath}}}}{\bold{\pink{*{Height }}}}`

Subsitute the required values,

For the first Box

Volume of first box

`\sf{ = 18 }{\sf{*{ 8 }}}{\sf{*{15}}}`

`\sf{ = 18 }{\sf{*{ 120 }}}`

`\bold{ = 2160 \:in.^(3)}`

Volume of Second box

`\sf{ = 196 }{\sf{*{ 10 }}}`

• Base area of second box already included length and breath into it

`\bold{ = 1960\: in.^(3)}`

From Above

• We can conclude that the first box has greater volume than the volume of second box

Now

We have to find , By how much the volume of first box is greater than the volume of second box

Therefore,

Volume of First Box - Volume of second box

`\sf{ = 2160 - 1960}`

`\bold{ = 200\: in.^(3)}`

Hence, The volume of first box is greater than second box by 200 in.³

Answer 2

Box 1 has the greater volume, by 200 in³

Explanation:

The largest of two volumes can be found by computing each volume and comparing the results.

Box 1

The volume is computed from dimensions by ...

V = LWH

V = (18 in)(8 in)(15 in) = 2160 in³

__

Box 2

The volume is computed from area and height by ...

V = Bh . . . . . where B is the base area, and h is the height

V = (196 in²)(10 in) = 1960 in³

__

Comparison

The units of the two volumes are the same, so we can decide which is larger by comparing the numbers. Box 1 has a volume that is more than 2000 in³, and Box 2 has a volume that is less than 2000 in³.

Box 1 has a greater volume

The amount by which the volume is greater can be found by subtracting the smaller volume from the larger:

2160 in³ -1960 in³ = 200 in³

Box 1 is larger by 200 in³

_____

Additional comment

The percentage by which Box 1 is larger than Box 2 can be found by multiplying 100% by the ratio of the difference to the Box 1 volume:

200/1960 × 100% ≈ 10.2%

Box 1 is about 10% larger than Box 2.