AREA
(i) The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonal of the rhombus is 22 cm, find the length of the other diagonal. (ii) The floor of a rectangular hall has a perimeter 250m. If the cost of paining the four walls at the rate of Rs 10 per m2 is Rs 1500. Find the height of the hall. (iii) A room is half as long again as it is broad. The cost of carpeting the room at Rs 3.25 per m2 is Rs 175.50 and the cost of papering the walls at Rs 1.40 per m2 is Rs 240.80. If 1 door and 2 windows occupy 8m2, find the dimensions of the room. (iv) A river 2m deep and 45m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute. (v) A closed cylinder has diameter 8cm and height 10cm. Find its total surface area and volume. (vi) The volume of a metallic cylinder pipe is 748cm3 . Its length is 14 cm and external diameter 18cm. Find its thickness. (vii) A cylindrical bucket, 28cm in diameter 72cm high is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank. (viii) A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its length is 25cm. The thickness of the metal is 8mm everywhere. Calculate the volume of the metal. (ix) The difference between outside and inside surface of a cylindrical metallic pipe 14cm long is 44cm2 . If the pipe is made of 99 cm3 . Find the outside and inner radii of the pipe.

Volume and surface area.
1. A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10cm and 6cm respectively. Find the volume of copper used in making the pipe. 2. The height of a right circular cylinder is 10.5m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the...

...Mathematics
Volume of Solids
Formulae for Volume of Solids
Cube | Cuboid | Triangular Prism | Cylinder | Cone | Pyramid | Sphere | AnyPrism |
s3 | lwh | ½bhl | Πr2h | 1/3πr2h | 1/3Ah | 4/3πr3 | Ah |
A = area of the base of the figure
s = length of a side of the figure
l = length of the figure
w = width of the figure
h = height of the figure
π = 22/7 or 3.14
1. Compute the volume of a cube with side 7cm.
Volume of...

...to study the gases present in the atmosphere.
6. It is mainly used in daily by pilots to measure the pressure in the air.
7. Area under a Curve and area in between the two curves are found by Integration.
8. Volume of Solid of Revolution explains how to use integration to find the volume of an object with curved sides, e.g. wine barrels.
9. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the...

...condition. Shakeology is easy to process --- just blending it with water or fresh milk could make it a lovely meal. It’s also easy to consume --- drink a cup of Shakeology might only takes one 5 minutes. As such one can easily control the time and volume of food intake and keep a healthy meal schedule no matter how busy he /she is.
* Hong Kong people need a product which can improve their diet while keeping their eating habit;
As said, Hong Kong people keep many Chinese...

...Calculating Tank Volume
Saving time, increasing accuracy
By Dan Jones, Ph.D., P.E.
C
alculating fluid volume in a horizontal or vertical cylindrical or elliptical tank can be complicated, depending on fluid height and the shape of the heads (ends) of a horizontal tank or the bottom of a vertical tank. Exact equations now are available for several commonly encountered tank shapes. These equations can be used to make rapid and accurate...

...(Term–II)
13
SURFACE AREAS AND VOLUMES
A. SUMMATIVE ASSESSMENT
(c) Length of diagonal =
TH
G
(a) Lateral surface area = 4l2 (b) Total surface area = 6l2 (c) Length of diagonal = 3 l 3. Cylinder : For a cylinder of radius r and height h, we have : (a) Area of curved surface = 2πrh
BR
O
ER
2. Cube : For a cube of edge l, we have :
O
YA L
TEXTBOOK’S EXERCISE 13.1 Unless stated otherwise, take =
22 . 7
Q.1. 2 cubes each of...

...quadratic polynomial are –
1 2
and have the same height. What is the ratio in their volumes? A 7. In the given figure, DE is parallel D E to BC and AD = 1 cm, BD = 2 cm. What is the ratio of the area of DABC to the area of DADE? B C 8. In the figure given below, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm, and CQ = 2 cm, what is the...

...Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and
semi-vertical angle 300 is πh3.
4. A window is in the form of a rectangle surmounted by a semi circular opening . The total perimeter
of the window is 10m. Find dimensions of the window to admit maximum light through the whole opening.
5. An open box with a square base is to be made out of a given quantity of sheet of area a2 .
Show that the maximum...

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