Height of the cylinder box = h = 35 cm Base radius of the cylinder box = r = 10 cm Width of metal sheet = 1m = 100 cm Area of metal sheet required = total surface area of the box Length x width =...

### The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its: (i) volume (ii) curved surface area

Let the original dimensions of the solid right cylinder be radius (r) and height (h) in cm. Then its volume = πr2h cm3and curved surface area = 2πrh Now, after the changes the new dimensions are:...

### The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.

The radius of a solid right cylinder (r) = 100 cm let the height of a solid right circular cylinder (h) = 100 cm The volume (original) of a solid right circular cylinder \[\begin{array}{*{35}{l}}...

### The height and the radius of the base of a cylinder are in the ratio 3:1. If its volume is 1029π cm3; find its total surface area.

The ratio between height and radius of a cylinder = 3:1 Volume = 1029π cm3 …….(i) the radius of the base = r Then, it’s height will be = 3r Volume \[\begin{array}{*{35}{l}} =\text{ }\pi...

### Find the total surface area of an open pipe of length 50 cm, external diameter 20 cm and internal diameter 6 cm.

Length of the open pipe = 50 cm Its external diameter = 20 cm It’s external radius (R) = 10 cm Its internal diameter = 6 cm => It’s internal radius (r) = 3 cm Surface area of pipe open from both...

### A cylindrical container with internal radius of its base 10 cm, contains water up to a height of 7 cm. Find the area of wetted surface of the cylinder.

Internal radius of the cylindrical container = 10 cm = r Height of water = 7 cm = h So, the surface area of the wetted surface \[\begin{array}{*{35}{l}} =\text{ }2\pi rh\text{ }+\text{ }\pi...

### A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm x 14 cm x 10.5 cm. Find the rise in level of the water when the solid is submerged.

Diameter of cylindrical container = 42 cm it’s radius (r) = 21 cm Dimensions of rectangular solid = 22cm x 14cm x 10.5cm The volume of solid = 22 x 14 x 10.5 cm3 ….. (i) Let the height of water = h...

### A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.

Inner radius of the pipe = r = 5/2 = 2.5 cm External radius of the pipe = R = Inner radius of the pipe + Thickness of the pipe \[=\text{ }2.5\text{ }cm\text{ }+\text{ }0.5\text{ }cm\text{ }=\text{...

### A cylinder has a diameter of 20 cm. The area of curved surface is 100 sq cm. Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.

The diameter of the cylinder = 20 cm the radius (r) = 10 cm and the curved surface area = 100 cm2 Height = h cm (i) Curved surface area \[\begin{array}{*{35}{l}} =\text{ }2\pi rh \\ 2\pi rh\text{...

### What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

External diameter of hollow cylinder = 20 cm So, it’s radius = 10 cm = R Thickness = 0.25 cm the internal radius \[=\text{ }\left( 10\text{ }-\text{ }0.25 \right)\text{ }=\text{ }9.75\text{...

### How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter.

Radius of the well = 2.8/2 = 1.4 m Depth of the well = 28 m Hence, the volume of earth dug out \[\begin{array}{*{35}{l}} =~\pi {{r}^{2}}h \\ =\text{ }\left( 22/7 \right)\text{ x }1.4\text{ x...

### A cylinder of circumference 8 cm and length 21 cm rolls without sliding for 4½ seconds at the rate of 9 complete rounds per second. Find: (i) distance travelled by the cylinder in 4½ seconds, and (ii) the area covered by the cylinder in 4½ seconds

Base circumference of cylinder (c) = 8 cm So, the radius \[=\text{ }c/2\pi \text{ }=\text{ }\left( 8\text{ x }7 \right)/\text{ }\left( 2\text{ x }22 \right)\text{ }=\text{ }14/11\text{ }cm\] Length...

### The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold?

The inner radius of the pipe = 2.1 cm Length of the pipe = 12 m = 1200 cm Volume of the pipe \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h\text{ }=\text{ }22/7\text{ x }{{2.1}^{2}}~x\text{...

### The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find: (i) the volume (ii) the total surface area.

Since, a circular cylinder whose Height, h = 20 cm and base radius, r = 7 cm (i) Volume of cylinder \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h\text{ }=\text{ }22/7\text{ }x\text{...