A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm.
Find the volume of wood in the entire stand (see figure).
"
Given:
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm.
To do:
We have to find the volume of the wood in the entire stand.
Solution:
Length of the cuboid pen stand $l = 15\ cm$
Breadth of the cuboid pen stand $b = 10\ cm$
Height of the cuboid pen stand $h = 3.5\ cm$
Therefore,
Volume of the cuboid pend stand $= lbh$
$= 15 \times 10 \times 3.5$
$= 525\ cm^3$
Radius of the conical depression $r = 0.5\ cm$
Height of the conical depression $h_1 = 1.4\ cm$
Volume of the conical depression $=\frac{1}{3} \pi r^2 h_1$
$=\frac{1}{3} \times \frac{22}{7} \times (0.5)^2 \times 1.4$
$=\frac{22 \times 0.5 \times 0.5\times0.2}{3}$
$=\frac{1.1}{3}$
$=0.366 \mathrm{~cm}^{3}$
The volume of four conical depressions $=4 \times$ Volume of the conical depression
$=4 \times 0.366$
$=1.47 \mathrm{~cm}^{3}$
The volume of wood in the entire pen stand $=$ Volume of the cuboidal pen stand $-$ Volume of 4 conical depressions
$=525-1.47$
$=523.53 \mathrm{~cm}^{3}$
The volume of the wood in the entire stand is \( 523.53 \mathrm{~cm}^{3} \).
Related Articles
- A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are \( 10 \mathrm{~cm} \times 5 \mathrm{~cm} \times 4 \mathrm{~cm} \). The radius of each of the conical depression is \( 0.5 \mathrm{~cm} \) and the depth is \( 2.1 \mathrm{~cm} \). The edge of the cubical depression is \( 3 \mathrm{~cm} \). Find the volume of the wood in the entire stand.
- The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
- If the areas of three adjacent faces of a cuboid are $8\ cm^2, 18\ cm^2$ and $25\ cm^2$. Find the volume of the cuboid.
- A wooden toy was made by scopoping out a hemisphere of same radius from each end of a solid cylinder.If the height of the cylinder is $10\ cm$, and its base is of radius $3.5\ cm$, find the volume of wood in the toy. [ use $\pi =\frac{22}{7}$]
- An wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is \( 10 \mathrm{~cm} \), and its base is of radius \( 3.5 \) \( \mathrm{cm} \), find the volume of wood in the toy. (Use \( \pi=22 / 7 \) )
- A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.[ use $\pi =\frac{22}{7}$].
- Find the volume of the cuboid having the following dimensions.\( 12 \mathrm{cm} \times 5 \mathrm{cm} \times 8 \mathrm{cm} \).
- A vessel in the shape of a cuboid contains some water. If three indentical spheres are immersed in the water, the level of water is increased by \( 2 \mathrm{~cm} \). If the area of the base of the cuboid is \( 160 \mathrm{~cm}^{2} \) and its height \( 12 \mathrm{~cm} \), determine the radius of any of the spheres.
- A box with lid is made of $2\ cm$ thick wood. Its external length, breadth and height are $25\ cm, 18\ cm$ and $15\ cm$ respectively. How much cubic cm of a liquid can be placed in it? Also, find the volume of the wood used in it.
- A solid piece of iron in the form of a cuboid of dimensions $49\ cm \times 33\ cm \times 24\ cm$, is moulded to form a solid sphere. Find the radius of the sphere.
- Find the volume of a sphere whose radius is $3.5\ cm$.
- A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius $\frac{3}{2}$ cm and its depth is $\frac{8}{9}$ cm. Calculate the ratio in the volume of metal left in the cylinder to the volume of the metal taken out in conical shape.
- A solid cuboid of iron with dimensions $33\ cm \times 40\ cm \times 15\ cm$ is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are $8\ cm$ and $7\ cm$ respectively. Find the length of pipe.
- The external dimensions of a closed wooden box are $48\ cm, 36\ cm, 30\ cm$. The box is made of $1.5\ cm$ thick wood. How many bricks of size $6\ cm \times 3\ cm \times 0.75\ cm$ can be put in this box?
- Find the number of spherical lead shots, each of diameter 6 cm that can be made from a solid cuboid of lead having dimensions $24\ cm\times22\ cm\times12\ cm$.
Kickstart Your Career
Get certified by completing the course
Get Started