The radius $\ ( in\ cm)$ of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
$( A) \ 4.2$ cm
$( B) \ 2.1$ cm
$( C) \ 8.4$ cm
$( D) \ 1.05$ cm
Given: A cube of edge $4.2\ cm$.
To do: To find out the radius of the largest right circular cone to be cut out from the cube.
Solution:
The largest right circular cone that can be cut out from the given cube, its diameter would be equal to side of the cube. And height of the cone would be also equal to the side of the given cube.
$\therefore$ Diameter of the cone $=$ side of the cube $=4.2\ cm$
Radius $=\frac{diameter}{2} =\frac{4.2}{2} =2.1\ cm$
$\therefore$ Option $( B)$ is correct.
Related Articles
- Find the volume of the largest right circular cone that can be cut out of a cube whose edge is \( 9 \mathrm{~cm} \).
- Find the volume of the largest right circular cone that can be fitted in a cube whose edge is $14\ cm$.
- The focal length of a spherical mirror of radius of curvature 30 cm is:(a) 10 cm (b) 15 cm (c) 20 cm (d) 30 cm
- Find the volume of the right circular cone with(i) radius \( 6 \mathrm{~cm} \), height \( 7 \mathrm{~cm} \)(ii) radius \( 3.5 \mathrm{~cm} \), height \( 12 \mathrm{~cm} \).
- Find the circumference and area of a circle of radius 4.2 cm.
- Find the total surface area of a right circular cone with radius $6\ cm$ and height $8\ cm$.
- If the focal length of a spherical mirror is 12.5 less cm, its radius of curvature will be:(a) 25 cm (b) 15 cm (c) 20 cm (d) 35 cm
- A hemisphere of lead of radius $7\ cm$ is cast into a right circular cone of height $49\ cm$. Find the radius of the base.
- Which of the following can be the sides of a right triangle?$(i).\ 2.5 cm,\ 6.5 cm,\ 6 cm.$$(ii).\ 2 cm,\ 2 cm,\ 5 cm.$$(iii).\ 1.5 cm,\ 2cm,\ 2.5 cm.$In the case of right-angled triangles, identify the right angles.
- From a point $Q$, the length of the tangent to a circle is $24$ cm and the distance of $Q$ from the centre is $25$ cm. The radius of the circle is(a) 7 cm(b) 12 cm(c) 15 cm(d) 24.5 cm
- The power of a lens is +2.0D. Its focal length should be :(a) 100 cm (b) 50 cm (c) 25 cm (d) 40 cm
- The largest sphere is to be carved out of a right circular cylinder of radius \( 7 \mathrm{~cm} \) and height \( 14 \mathrm{~cm} \). Find the volume of the sphere.
- A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
- Find the volume of a right circular cone with height $21\ cm$ and slant height $28\ cm$.
- A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Kickstart Your Career
Get certified by completing the course
Get Started