Maths question about surface area?

Question

Im really bad at everything to do with surface area, could someone please explain this question to me? :)

six cubes each have a surface area of 24cm²
they are joined together to make a cuboid
what could the surface area of this cuboid be
there are two different answers

thanks!

Answer 1

The 6 cubes each have 6 faces so the area of each face is 4 cm^2.
The cubes could be arranged in either a 2x3 pattern or a 6X1 long skinny pattern.

With the 2x3 shape you will have 22 sides of the cubes showing. Draw this and you will see - 6 on the top, 6 on the bottom and 10 on the sides.
So the surface area will be 22x4=88cm^2.

With the 6x1 shap, you will have 26 sides showing. Do the drawing so you can count them. 6 on the top, 6 on the bottom, 6 along each long side and 2 on the ends. So the surface area is 26x4 = 104 cm^2

Answer 2

The cuboid must have the dimensions 1*6 (cuboid A) or 2*3 (cuboid B).

A has 12 faces along dimension X, 12 along Y, and 2 along Z, for a total of 26 cube faces making up its surface area. B has 12, 6, and 4 faces along the same dimensions, respectively, for a total of 22 faces.

The surface area of one face is (24 cm^2)/6 faces=4 cm^2.

Therefore, the cuboid may have a surface area of either 26*4=104 cm^2 or 22*4=88 cm^2.

Answer 3

The cubes have SA 24cm^2 = 6r^2, so they have a side length of r = √(24/6) = 2 cm.

If you join them together in a 2×3 block, you will get a 2cm×4cm×6cm cuboid. There are two 2×4 faces with a combined surface area of 2(2)(4) = 16 cm^2, two 4×6 faces with combined SA 2(4)(6) = 48 cm^2, and two 2×6 faces with combined SA 2(2)(6) = 24 cm^2. So the total SA is 16+48+24 = 88 cm^2.

If you join the cubes in a 1×6 block you will have a 2cm×2cm×12cm cuboid. There are four 2×12 faces, with combined SA 4(2)(12) = 96 cm^2, and two 2×2 faces with combined SA 2(2)(2) = 8 cm^2 for a total of 104 cm^2.

Answer 4

a cube has six sides, therefore each side of a cube is 4cm².
so there can be 2 ways to join the six cubes to form a cuboid
1) to join all six cubes together forming a straight line.now to calculate the surface area we only add the surface area of the number of sides (4cm²) tat can be seen. so we have 26 cube sides therefore surface area=26 x 4 =104cm²

2) to join 3 cubes together and join the other three cubes to the longer side. which will make it a 2 by 3 cuboid. total no. of cube sides facing outside = 22
surface area= 22 x 4 =88cm²

u have to imagine the cuboid or draw it to be much visual

Answer 5

Total surface area of the cubes is
24*6 cm^2
=144 cm^2
now,you know that a cube has six surface areas ,all of equal areas.therefore,we can say that each sueface area of each of the cube is 24/6 or 4 cm^2
Now,if we join them together.
one each surface area of the first and the last cubes will not be available alongwith two surface areas each of 2nd,3rd,4th and 5th cube
surface area will be reduced by 10*6 or 60 cm^2 if they are joined longitudinally
we can also join them vertically,three each in two rows
Please calculate the loss of surface area yourself.in this way only 6 surface areas will be less

Answer 6

if the arrangement is 2X3;
let the side length be x of one cube.
now,
surface area of one cube= 6a^2=24cm^2
=>a=2cm
now the length= 3Xa=3a
and breath=2Xa=2a
and width=2xa=2a
now the surface area=2(lb+bw+lw)=2(3aX2a+2aX2a+2aX3a)
=2(6a^2+4a^2+6a^2)=2(16a^2)=32a^2.(ans)

if the arrangement is 1X6
let the side length be x of one cube.
now,
surface area of one cube= 6a^2=24cm^2
=>a=2cm
now the length= 6Xa=6a
and breath=1Xa=a
and width=1xa=a
now the surface area=2(lb+bw+lw)=2(6aXa+aXa+aX6a)
=2(6a^2+a^2+6a^2)=2(13a^2)=26a^2.(ans)

Answer 7

C Plonking the dimensions of the cylinder (0.5 feet radius, 5 feet height) into the given formula yields 17.27 square feet.

Answer 8

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