Maharashtra Board Solutions for Chapter: Mensuration, Exercise 5: Problem set 7

Some plastic balls of radius $1 \mathrm{cm}$ were melted and cast into a tube. The thickness, length and outer radius of the tube were $2 \mathrm{cm}, 90 \mathrm{cm}$ and $30 \mathrm{cm}$ respectively. How many balls were melted to make the tube ?

A metal parallelopiped of measures $16 \mathrm{cm}\times 11 \mathrm{cm}\times 10 \mathrm{cm}$ was melted to make coins. How many coins were made if the thickness and diameter of each coin was $2 \mathrm{mm}$ and $2 \mathrm{cm}$ respectively ?

The diameter and length of a roller is $120 \mathrm{cm}$ and $84 \mathrm{cm}$ respectively. To level the ground, $200$ rotations of the roller are required. The expenditure to level the ground at the rate of $₹10$ per $\mathrm{square} \mathrm{m}$ is $₹k$. Find the value of $k$.

A cylindrical bucket of diameter $28 \mathrm{cm}$ and height $20 \mathrm{cm}$ was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was $14 \mathrm{cm},$ what was the base area of the cone ?

The radius of a metallic sphere is $9 \mathrm{cm}.$ It was melted to make a wire of diameter $4 \mathrm{mm}.$ Find the length of the wire.

In the figure, seg $\mathrm{AB}$ is a chord of a circle with centre $\mathrm{P}.$ If $\mathrm{PA}=8 \mathrm{cm}$ and distance of chord $\mathrm{AB}$ from the centre $\mathrm{P}$. is $4 \mathrm{cm},$ find the area of the shaded portion.

In the figure $7.48,$ square $\mathrm{ABCD}$ is inscribed in the sector $\mathrm{A}-\mathrm{PCQ}.$ The radius of sector $\mathrm{C}-\mathrm{BXD}$ is $20 \mathrm{cm}.$ Complete the following activity to find the area of shaded region.

In the figure $7.49,$ two circles with centres $\mathrm{O}$ and $\mathrm{P}$ are touching internally at point $\mathrm{A}.$ If $\mathrm{BQ}=9,\mathrm{DE}=5,$ complete the following activity to find the radii of the circles.