Question

Lucas built a composite solid by joining 12 identical blocks, with dimensions 4 inches by 5 inches by 7 inches, into three rows of four as shown.


12 blocks are in 3 rows of 4. Each block is 4 inches by 5 inches by 7 inches.


What is the total surface area of the composite solid?
521 square inches
1,042 square inches
1,072 square inches
1,992 square inches

Answer 1

Answer

the answer is b. im not sure though

Step-by-step explanation:

Answer 2

1042 square inches is the total surface area of composite solids.

It is clear from the image that the resulting composite solid is a cuboid.

whose sides are as follows

Across the length, there are 3 blocks along the side of 7 inches each.

$Length = 7 \times 3 = 21\ inch$

Width = 5 inch

Across the height, there are 4 blocks along the side of 4 inches each.

$Height = 4 \times 4 = 16\ inch$

What is the total surface area of a cuboid?

$\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)$

We know that the total surface area of a cuboid is,

$\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)\Rightarrow 2 (21 \times 5 + 16 \times 21 + 16 \times 5 )\\\Rightarrow 2 (105 + 336+80)\\\Rightarrow 2 \times 521\\\Rightarrow 1024$

Therefore, the total surface area = 1024 square inches.

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