ML Aggarwal Solutions Class 9 Mathematics Solutions for Mensuration Exercise 16.4 in Chapter 16 - Mensuration

Question 9 Mensuration Exercise 16.4

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.


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}


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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