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anygoal [31]
3 years ago
12

5) A rectangular box 25cm by 20cm by 15cm internally is made of wood

Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0

Answer:

The volume of the wood used is 1,116\ cm^3

Step-by-step explanation:

<u>The Volume of a Rectangular Cuboid</u>

In a rectangular cuboid, all angles are right, and the opposite faces are equal.

The volume of a cuboid of dimensions a,b,c is:

V=a.b.c

The rectangular box is made of wood with externals dimensions of 25 cm by 20 cm by 15 cm.

The external volume of the box is:

V_e=(25)*(20)*(15)=7,500\ cm^3

The walls of the box are 0.5 thick each, this means that the internal dimensions are 1 cm less than the external dimensions, including the lid.

Thus the internal volume is:

V_i=(24)*(19)*(14)=6,384\ cm^3

The volume of the wood used is the difference between the external and the internal volumes:

V_w=7,500\ cm^3-6,384\ cm^3=1,116\ cm^3

The volume of the wood used is \mathbf{1,116\ cm^3}

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Help please! Could you explain it too?
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Answer:

a) not proportional

b) proportional; k = -\frac{3}{5}

Step-by-step explanation:

a) for any proportional equation, the line must pass through the origin. The equation in a) is y = 4x + 1, and the '+1' is the y-intercept. This means that the line does not pass through the origin, so x and y cannot increase by the same amount (i.e. they are not proportional).

Another way to determine this is is to use the y = kx base. If you have an equation that fits that it's likely proportional.

Here, if the equation was only y = 4x then it'd be proportional because u can see that k = 4. This is not the equation though, and the 4x + 1 doesn't fit to the y = kx formula so it can't be proportional.

b) straight away you can see that there's no 'c' term (y = mx + c) which means the y-intercept is 0, so the line passes through the origin. While this does not immediately mean the line is proportional, you can make sure that it is by checking it fits with the y = kx equation.

y = -(3/5)x fits with y = kx, with k being -3/5

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