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ML Aggarwal Solutions Class 9 Mathematics Solutions for Mensuration Exercise 16.4 in Chapter 16 - Mensuration
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A cube of a metal of 6 cm edge is melted and cast into a cuboid whose base is 9 cm × 8 cm. Find the
height of the cuboid.
Answer:
It is given that
Edge of melted cube = 6 cm
Volume of melted cube = 6 cm × 6 cm × 6 cm = =216 \mathrm{cm}^{3}
Dimensions of the cuboid are
Length = 9 cm
Breadth = 8 cm
h cm is the height
We know that
Volume of cuboid = l × b × h
Substituting the values
= 9 × 8 × h
=72 \mathrm{h} \mathrm{cm}^{3}
Here
The volume of cuboid = Volume of the melted metal cube
Substituting the values
72h = 216
h = 216/72 = 3 cm
Therefore, the height of the cuboid is 3 cm.
Video transcript
"hello and welcome idea students
i am rishabh the math tutor on leader
and i'm here
the new question it is a cube of a metal
six centimeter edge is melted and cast
into a cuboid
whose base is 9 centimeter into 8
centimeter
find the height of the cuboid so without
wasting much time let's have a look at
the solution
so we know that we have been given
edge of magic
q
is six centimeter
therefore the volume of the
melted cube
is equal to side q just beyond that
volume of cube is nothing but the side
cube
so that means x cube which is nothing
but
2 1 6
centimeter cube also we have been given
the dimensions of the cuboid
whose base is nine centimeter into eight
centimeter
and we are supposed to find out the
height
so the dimensions
of cuboid are
the length is given as 9 centimeter
the width is given as 8 centimeter
and let
h with the height
so the volume of
we all know is that l into b into h
we substitute the values so we get 9
into 8 into
h and since the cube hasn't melted
to cast to cast into a cuboid
that means the cube has been melted to
make a cuboid that means the volume
remains
the same therefore
the volume of cube
is equals to volume of
melted
or numerated as volume of cuboid
is equals to volume of
welted q all metal
anything that you like
so substituting the value we get 72 into
h
is equals to 216.
so height is equal to 216 divided by 72
which is nothing but equals to 3
centimeter that means the height of the
cuboid is
three centimeter so i hope
my students record this question well do
not forget to hit the subscribe button
you can also share your doubts in the
comment section see you next time bye
bye"
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