Tag: volume of solids

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Questions Related to volume of solids

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

The radius of a cone is $\sqrt2$ times the height of the cone. A cube of maximum possible volume is cut from the same cone. What is the ratio of the volume of the cone to the volume of the cube?

  1. $3.18\pi$
  2. $2.25\pi$
  3. $2.35$

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cube here will be inscribed in a cone as a square is in isosceles triangle.
Let the height of the cone be $h$
Radius=$\sqrt2 h$
Volume of cone=$\dfrac{1}{3}\pi r^2h$
                           =$\dfrac{2\sqrt 2}{3}\pi h^3$
Let the side of the cube be x,the top of the cone above it has the sign $(h-x)$ and radius $\dfrac{x}{2}$
Using properties of similar triangle $\dfrac { \dfrac { x }{ 2 }  }{ h-x } =\dfrac{\sqrt2 h}{h}$
                                                            $=\sqrt 2 x$
                                                             $=\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } $
Volume of the cube=$\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } $
Ratio of the volume of the cone to volume of the cube=$\dfrac { \dfrac { 2\sqrt { 2 }  }{ 3 } \pi h^{ 3 } }{ (\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } )^ 3 } $
                                            $=\dfrac{\pi(2\sqrt { 2 } +1  )^ 3)}{24}$
                                            $=2.35\pi$

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

If a box is $\dfrac{1}{4}$ filled contains $5$ small cubes each of volume $1$ cubic units then find out the volume of the box.

  1. $25$ cu.
  2. $20$ cu.
  3. $15$ cu.
  4. $5$ cu.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the box is $\dfrac {1}{4}$ filled with  the given cubes , we need to multiply the total volume of the given cubes by $4$ to get the total volume of thr box.

Volume of one cube is $1 cu.$
$\therefore $ Volume of 5 cubes will be $5\times 1 cu.=5cu.$
$\therefore $ Volume of the box will be $4\times 5 cu.=20cu.$

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

How many small cubical blocks side $5$cm can be cut from a cubical block whose each edge measure $20$cm?

  1. $56$
  2. $48$
  3. $64$
  4. $52$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number of small cubes that can be cut is found by dividing the volume of the large cube by the volume of one small cube. Volume of the large cube is 20 x 20 x 20 = 8000 cm^3, and the volume of one small cube is 5 x 5 x 5 = 125 cm^3. Dividing 8000 by 125 gives 64.

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

how many bricks are required to build a wall 15 m long 3 m high and 50 cm thick ,if each brick measures 25 cm by 12 cm by 6 cm?

  1. $16500$
  2. $14500$
  3. $12500$
  4. $10500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, convert all wall dimensions to centimeters: length = 1500 cm, height = 300 cm, thickness = 50 cm. The volume of the wall is 1500 * 300 * 50 cm^3. The volume of a single brick is 25 * 12 * 6 cm^3. Dividing the total wall volume by the volume of one brick gives (1500 * 300 * 50) / (25 * 12 * 6) = 12500 bricks.

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

If the volumes of two cubes are in the ratio $8:1$, then the ratio of their edges is

  1. $8:1$
  2. $2\sqrt 2:1$
  3. $2:1$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $V _1$ and $V _2$ be two volume of cubes.

$l _1$ and $l _2$ be edges of the two cubes.
We know that,
Volume of cube $V=l^3$
So,
$\Rightarrow$  $\dfrac{V _1}{V _2}=\dfrac{l _1^3}{l _2^3}$

$\Rightarrow$  $\dfrac{8}{1}=\left(\dfrac{l _1}{l _2}\right)^3$             [ Given ]

$\therefore$  $\dfrac{l _1}{l _2}=\dfrac{2}{1}$

$\therefore$  Ratio of their edges is $2:1$.

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

The volume of a cube whose surface area is $96{cm}^{2}$, is

  1. $16\sqrt 2{cm}^{3}$
  2. $32{cm}^{3}$
  3. $64{cm}^{3}$
  4. $216{cm}^{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $l$be the side of cube.

Surface area of cube $=6l^2$
$\Rightarrow$  $96=6l^2$                      [ Given ]
$\Rightarrow$  $l^2=16$
$\therefore$  $l=4\,cm$
Now,
$\Rightarrow$  Volume of cube $=l^3$
                                  $=(4)^3$
                                  $=64\,cm^3$

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

If each edge of a cube, of volume $V$, is doubled, then the volume of the new cube is

  1. $2V$
  2. $4V$
  3. $6V$
  4. $8V$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $a$ be the initial edge of the cube.

So, 
Volume of cube $V=a^3$
In the new cube,
Let $a'$ be the edge of new cube
$\therefore$  $a'=2a$               [ Given ]
Volume of new cube,
$V'=(a')^3$
      $=(2a)^3$
      $=8a^3$
      $=8V$                        [ Since, $a^3=V$ ]
Volume of the new cube is $8V.$