Mahabir Singh Solutions for Chapter: Surface Areas and Volumes, Exercise 1: MATHEMATICAL REASONING

A right circular cone is $4.1 \mathrm{cm}$ high and the radius of its base is $2.1 \mathrm{cm}$. Another right circular cone is $4.3 \mathrm{cm}$ high and the radius of the base is $2.1 \mathrm{cm}$. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.

The number of solid spheres, each of diameter $6 \mathrm{cm}$ that could be moulded to form a solid metal cylinder of height $45 \mathrm{cm}$ and diameter $4 \mathrm{cm}$, is 

The height of a cone is $30 \mathrm{cm}$. A small cone is cut off at the top by a plane parallel to the base. If its volume be $1/27$ of the volume of the given cone, at what height above the base is the section made?

A cuboidal metal of dimensions $44 \mathrm{cm}\times 30 \mathrm{cm}\times 15 \mathrm{cm}$ was melted and cast into a cylinder of height $28 \mathrm{cm}$. Its radius is 

Study the question and the statements given below and decide which of the statement(s) is$/$are necessary to answer the question.
What is the capacity of the cylindrical tank?
I. The area of the base is  $61,600 \mathrm{sq}.\mathrm{cm}.$
II. The height of the tank is $1.5$ times the radius.
Ill. The circumference of base is $880 \mathrm{cm}.$

A cylindrical tub of radius $5 \mathrm{cm}$ and length $9.8 \mathrm{cm}$ is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is $3.5 \mathrm{cm}$ and the height of the cone outside the hemisphere is $5 \mathrm{cm}$, find the volume of water left in the tub. (Take $\pi =22/7$)

Find the maximum Volume of a Cone that can be carved out of a solid Hemisphere of radius $r$.

A cylindrical vessel of diameter $4 \mathrm{cm}$ is partly filled with water. $300$ lead balls are dropped in it. The rise in water level is $0.8 \mathrm{cm}$. The diameter of each ball is