3D Geometrical Shapes

The ratio of heights of two cylinders is $3:2$and the ratio of their radii is $6:7$. What is the ratio of their curved surface areas?

If the base radius and the height of a right circular cone are increased $40\%$, then find the net $\%$ increase in volume _____.

Three metallic cubes whose edges are in the ratio $3:4:5$ are melt to from a single cube whose diagonal is $12\sqrt{3} \mathrm{cm}$. What are the lengths of the edges $(\mathrm{in} \mathrm{cm})$ of the three cubes?

Three cubes of copper are melted and formed into a single cube of edge $12 \mathrm{cm}$, if the edge of one cube is $6 \mathrm{cm}$ and the edge of the second cube is $10 \mathrm{cm}$ then the edge of the third cube? The surface area of the new cube formed is _____.

In a quadrilateral, half of the product of the sum of the lengths of parallel sides and the parallel distance between them gives the area of:

How much length of the iron sheet $11 \mathrm{cm}$ wide is required for making an open cylinder $15 \mathrm{cm}$ height and$7 \mathrm{cm}$ as base radius?

A rectangular box P is inscribed in a sphere of radius $r \mathrm{cm}$. The surface area of P is $384 {\mathrm{cm}}^2$. and the sum of the length of its $12$ edges is $112 \mathrm{cm}$. Then $r (\mathrm{in} \mathrm{cm}.)$ is equal to _____.

A cylindrical container is filled with ice cream. Its diameter is $12 \mathrm{cm}$ and its height is $15 \mathrm{cm}$. The whole ice cream is distributed among $10$ children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, the diameter of the ice cream cone is_____

Two circular cylinders of equal volume have their heights in the ratio $1:2$. The ratio of their radii is _____.

A sphere is inscribed in a cubical box such that the sphere is tangent to all six faces of the box. What is the ratio of the volume of the cubical box to the volume of sphere?

The ratio of the volumes of two circular cylinders is $a:b$, and the ratio of their heights is $b:a$ .  Find the ratio of their radii.

A room is $12 \mathrm{m}$ long $9 \mathrm{m}$ broad and $8 \mathrm{m}$ high.The length of the longest bamboo pole that can be placed in it will be _____.

What is the total surface area of a one-side open cubical box of outer side of length $5 \mathrm{cm}$. and thickness $0.5 \mathrm{cm}$?

The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is;

The diameter of the base of a right circular cone is $6 \mathrm{cm}$ and its perpendicular height is $3\sqrt{3} \mathrm{cm}$. Find the slant height of the cone.

Consider the following to the question that follow:

A chord of length $l$ of a circle makes an angle ${90}^{\mathrm{o}}$ at the centre of the circle.

What is the area of the minor segment?

A tub is in the shape of a frustum of a cone. The radii of two circular ends of the tub are $105 \mathrm{cm}$ and $42 \mathrm{cm}$. If the vertical height of the tub is $16 \mathrm{cm}$, what is its slant height ?

The side faces of a pyramid are always:

The portion of a ditch $48 \mathrm{m}$ long, $16.5 \mathrm{m}$ wide and $4 \mathrm{m}$ deep that can be filled with stones and earth available during excavation of a tunnel, cylindrical in shape, of diameter $4 \mathrm{m}$ and length $56 \mathrm{m}$ is (take $\pi =\frac{22}{7}$)

Which shape is formed by rotating a right triangle about its height or altitude?