Ajay Kumar Solutions for Chapter: Numerical Ability, Exercise 19: Practice set

The edges of a cube are $12 \mathrm{cm}$ long. An ant moves on the cube surface from point A to point B along the path shown. The length of the ant's path is?

Anita put $120$ identical cubes together to form a rectangular prism. She then painted all $6$ faces of the prism. Once the paint had dried she disassembled the cubes and found that $24$of the cubes had not been painted on any face. The surface area of the prism she formed was?

What is the maximum number of rectangular wooden blocks with dimensions $20 \mathrm{cm}\times 30 \mathrm{cm}\times 40 \mathrm{cm}$ that could fit into a rectangular box with inner dimensions $40 \mathrm{cm}\times 60 \mathrm{cm}\times 80 \mathrm{cm}$?

Suppose we make $\mathrm{N}$ identical smaller spheres from a big sphere. The total surface area of the smaller spheres is $\mathrm{X}$ times the total surface area of the big sphere, where $\mathrm{X}$ is?

A cuboid shaped slab of iron whose dimensions are $55 \mathrm{cm}\times 40 \mathrm{cm}\times 15 \mathrm{cm}$ is melted and recast into a pipe. The outer diameter and thickness of the pipe are $8 \mathrm{cm}$ and $1 \mathrm{cm}$ respectively. Find the length of the pipe.

A cylinder of radius $1 \mathrm{cm}$ and height $1 \mathrm{cm}$ is broken into three pieces. Which of the following must be true?

A cylindrical pail containing water drains Into a cylindrical tub $40 \mathrm{cm}$ across and $50 \mathrm{cm}$ deep, while resting at an angle of $45°$ to the horizontal, as shown. How deep is the water in the tub when its level reaches the pail?

A company makes solid blocks with square bases. The volume of this block is $640 {\mathrm{cm}}^3$. Its height is $10 \mathrm{cm}$. The cost of painting all the faces of this block at $₹. 15$per ${\mathrm{cm}}^2$ is?