Exercise 17 E
Question 1
Copy and complete the table $\left(\pi=\frac{22}{7}\right)$
| (a) | (b) | (c) | |
| Radius of the circle (cm) | 7 | 14 | 21 |
| Height (cm) | 8 | 16 | 40 |
| Volume $(cm^3)$ | ? | ? | ? |
2. The volume of a cylinder is $660 \mathrm{~cm}^{3}$. Find its height if its radius is $5 \mathrm{~cm}$.
3. The volume of a cylinder is $448 \pi \mathrm{cm}^{3}$ and height $7 \mathrm{~cm}$. Find its lateral (curved) surface area and total surface area.
4. The volume of a right circular cylinder is $1100 \mathrm{~cm}^{3}$ and the radius of its base is $5 \mathrm{~cm}$. Find its curved surface area. ( $\pi=22 / 7)$
5. A solid cylinder has total surface area of $462 \mathrm{sq} \mathrm{cm}$. Its curved area is one third of its total surface area. Find the volume of the cylinder. (Take $\left.\pi=\frac{22}{7}\right)$
6. If base radius of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
7. A cylindrical tank has a capacity of $6160 \mathrm{cu} \mathrm{cm}$. Find its depth if its radius is $14 \mathrm{~cm}$. Calculate the cost of painting its curved outer surface at the rate of $₹ 3$ per sq $\mathrm{cm}$. (Take $\left.\pi=\frac{22}{7}\right)$
8. The circumference of the base of a cylindrical vessel is $132 \mathrm{~cm}$ and its height is $25 \mathrm{~cm}$. How many litres of water can it hold ?
9. A hollow cylindrical tube open at both ends is made of iron $3 \mathrm{~cm}$ thick. If the external diameter be $56 \mathrm{~cm}$ and the length of the tube be $182 \mathrm{~cm}$, find the number of cubic $\mathrm{cm}$ in it.
10. A well $14 \mathrm{~m}$ inside diameter is dug $15 \mathrm{~m}$ deep. Earth taken out is spread all around to a width of $7 \mathrm{~m}$ to form an embankment. Find the height of the embankment.
11. The rain falls $10 \mathrm{~cm}$ on a particular day. The rain water that falls on a roof $70 \mathrm{~m}$ long and $44 \mathrm{~m}$ wide was collected in a cylindrical tank of radius $14 \mathrm{~m}$. Find
(i) volume of the water that falls on the roof.
(ii) rise of water level in the tank due to rain water.
[Hint. Volume of rain water $=l \times b \times h=70 \times 44 \times \frac{1}{10}=308 \mathrm{~m}^{3}$
Let $h \mathrm{~m}$ be the rise in water level. Then volume of the cylindrical column of water of height $h=$ volume of rain water) i.e., $\pi \times 14^{2} \times h=308$. ]
Multiple Choice Questions (MCQs)
12. The curved surface of a cylindrical pillar is $264 \mathrm{~m}^{2}$ and its volume is $924 \mathrm{~m}^{3}$. The diameter of the pillar is
(a) $5 \mathrm{~m}$
(b) $9 \mathrm{~m}$
(c) $10 \mathrm{~m}$
(d) $14 \mathrm{~m}$
13. The radii of two cylinders are in the ratio 2: 3 and their heights are in the ratio $5: 3$. The ratio of their volumes is
(a) $27: 20$
(b) $20: 27$
(c) $4: 9$
(d) $9: 4$
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