Exercise 17 C
Question 1
1. A solid cube of edge $20 \mathrm{~cm}$ is melted and cast into a cuboid whose base measures $25 \mathrm{~cm}$ by $20 \mathrm{~cm}$. Find the height of the cuboid.
2. A rectangular block of metal measuring $4 \mathrm{~cm}$ by $5 \mathrm{~cm}$ by $6 \mathrm{~cm}$ was melted down to make a block $8 \mathrm{~cm}$ long by $3 \mathrm{~cm}$ wide. How high was the block ?
3. How many bricks, each of dimensions $25 \mathrm{~cm} \times 16 \mathrm{~cm} \times 10 \mathrm{~cm}$ will be needed to build a wall $24 \mathrm{~m}$ long, $6 \mathrm{~m}$ high and $0.4 \mathrm{~m}$ thick.
4. The inside measurements of a cardboard box are $1 \frac{1}{2} \mathrm{~m}$ by $\frac{3}{4} \mathrm{~m}$ by $60 \mathrm{~cm}$. How many books, $20 \mathrm{~cm}$ by $10 \mathrm{~cm}$ by $7.5 \mathrm{~cm}$ each can be arranged in the box ?
5. A class room is $12 \mathrm{~m}$ long, $5 \mathrm{~m}$ wide and $3 \mathrm{~m}$ high. How many pupils should it be used for if each pupil required $5 \mathrm{~m}^{3}$ of air space ?
6. How many lead cubes of side $2 \mathrm{~cm}$ could be made from a lead cube of side $8 \mathrm{~cm}$ ?
7. How many wooden cubical blocks of edge $20 \mathrm{~cm}$ can be cut from a log of wood of size $8 \mathrm{~m}$ by $5 \mathrm{~m}$ by $80 \mathrm{~cm}$, assuming there is no wastage.
8. A cuboid of dimensions $10 \mathrm{~cm}$ by $2 \mathrm{~cm}$ by $2 \mathrm{~cm}$ is divided into 5 cubes of edge $2 \mathrm{~cm}$. Find the ratio of the total surface area of the cuboid and that of the cubes.
9. A pit $5 \mathrm{~m}$ long and $3.5 \mathrm{~m}$ wide is dug to a certain depth. If the volume of earth taken out of it is $14 \mathrm{~m}^{3}$, what is the depth of the pit ?
10. The dimensions of a field are $15 \mathrm{~m}$ by $12 \mathrm{~m}$. A pit $7.5 \mathrm{~m}$ long, $6 \mathrm{~m}$ wide and $1.5 \mathrm{~m}$ deep is dug at one corner of the field. The earth removed is evenly spread over the remaining area of the field. Calculate the rise in the level of the field.
Multiple Choice Questions (MCQs)
11. How many bricks, each measuring $25 \mathrm{~cm} \times$ $11.25 \mathrm{~cm} \times 6 \mathrm{~cm}$ will be needed to build a wall $8 \mathrm{~m} \times 6 \mathrm{~m} \times 22.5 \mathrm{~cm}$.
(a) 5600
(b) 6000
(c) 6400
(d) 7200
12. A cube of lead with edges measuring $6 \mathrm{~cm}$ each is melted and formed into 27 equal cubes. What will be the length of the edges of the new cubes?
(a) $3 \mathrm{~cm}$
(b) $4 \mathrm{~cm}$
(c) $2 \mathrm{~cm}$
(d) None of these
