Question

A cone of height 21 cm and base radius 6 cm is made up of modelling clay. A child reshapes it in the form of a cuboid of length 9 cm and width 8 cm. Find the height of the cuboid.

Answer 1

volume of cone = volume of cuboid

1/3πr^2h=l*b*h

1/3*22/7*6*6*21=9*8*h

792/9*8=h

=11

height of cuboid=11cm

Answer 2

Answer:

The height of the cuboid is 11 cm.

Step-by-step-explanation:

We have given the dimensions of a cone and cuboid.

The cone was reshaped into the cuboid.

As the cone and cuboid both were made by a modelling clay, their volume must be equal.

$\sf\:For\:cone,\\\\\\\bullet\sf\:height\:(\:h\:)\:=\:21\:cm\\\\\\\bullet\sf\:radius\:(\:r\:)\:=\:6\:cm\\\\\\\sf\:For\:cuboid,\\\\\\\bullet\sf\:length\:(\:l\:)\:=\:9\:cm\\\\\\\bullet\sf\:width\:(\:b\:)\:=\:8\:cm\\\\\\\bullet\sf\:height\:(\:h\:)$

Now,

$\pink{\sf\:Voulme\:of\:cone\:=\:Volume\:of\:cuboid}\\\\\\\implies\sf\:\dfrac{1}{3}\:\pi\:r^2\:h\:=\:l\:\times\:b\:\times\:h\\\\\\\implies\sf\:\dfrac{1}{3}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6\:\times\:21\:=\:9\:\times\:8\:\times\:h\\\\\\\implies\sf\:h\:=\:\dfrac{1}{3}\:\times\:\dfrac{22}{\cancel7}\:\times\:6\:\times\:6\:\times\:\cancel{21}\:\times\:\dfrac{1}{9}\:\times\:\dfrac{1}{8}\\\\\\\implies\sf\:h\:=\:\dfrac{1}{\cancel3}\:\times\:22\:\times\:36\:\times\:\cancel{3}\:\times\:\dfrac{1}{9}\:\times\:\dfrac{1}{8}\\\\\\\implies\sf\:h\:=\:22\:\times\:\cancel{36}\:\times\:\dfrac{1}{\cancel9}\:\times\:\dfrac{1}{8}\\\\\\\implies\sf\:h\:=\:\dfrac{22\:\times\:\cancel{4}}{\cancel{8}}\\\\\\\implies\sf\:h\:=\:\cancel{\dfrac{22}{2}}\\\\\\\implies\boxed{\red{\sf\:h\:=\:11\:cm}}\\\\\\\therefore\underline{\sf\:The\:height\:of\:cuboid\:is\:11\:cm\:.\:}$

Additional Information:

1. Cone:

Any three dimensional figure having two surfaces with base circular in shape is called as cone.

2. Examples of conical objects:

Conical tent, ice - cream cone, sharpened end of pencil, etc are some examples of conical objects.

3. Important formulae related to cone:

A cone having height $h$, slant height $l$ and radius $r$ has following formulae:

$\sf\:1.\:Area\:of\:base\:=\:\pi\:r^{2}\\\\\sf\:2.\:l^{2}\:=\:r^{2}\:+\:h^{2}\:\:\:\:or\:\:\:l\:=\:\sqrt{r^{2}\:+\:h^{2}}\\\\\sf\:3.\:Curved\:surface\:area\:=\:\pi\:r\:l\\\\\sf\:4.\:Total\:surface\:area\:=\:\pi\:r\:(\:r\:+\:l\:)\\\\\sf\:5.\:Volume\:=\:\dfrac{1}{3}\:\pi\:r^{2}\:h$

4. Formula for volume of cuboid:

$\large{\boxed{\red{\sf\:Volume\:of\:cuboid\:=\:length\:\times\:breadth\:\times\:height}}}$