A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12 cm × 7 . 5 cm . If 1 12 of the total volume of the wall consists of mortar how many bricks are there in a wall?

Given that, Length of the wall = 15 m = 1500 cm , width of the wall = 30 cm , height of the wall = 4 m = 400 cm is made of bricks. We know that, Volume of a cuboid = length × breadth × height So, the volume of the wall = 1500 × 30 × 400 = 18000000 cm 3 Given that 1 12 volume of wall consist of mortar volume of the wall consisting of mortar = 1 12 × 18000000 cm 3 = 15000000 cm 3 So that volume of the wall consisting of bricks = 18000000 - 15000000 = 16500000 cm 3 Volume of each brick = ( 22 × 12 × 7 . 5 ) = 1980 cm 3 Now the number of brick in wall = Total volume of bricks Volume of a single brick Number of bricks in wall = 16500000 1980 = 8333 (Apprx) Hence, there are 8 , 333 (approx) bricks in the wall

If V is the volume of a cuboid of dimensions a × b × c and S is its surface area, then prove that 1 V = 2 S 1 a + 1 b + 1 c .

Given: V is the Volume of the cuboid, S is the Surface area of the cuboid and a , b , c are the dimensions of the cuboid. To prove: 1 V = 2 S 1 a + 1 b + 1 c . We know that, S = 2 a b + b c + c a and V = a b c 1 V = 1 a b c Multiply the numerator and denominator by S . 1 V = S S a b c 1 V = 2 a b + b c + c a S a b c {Since, S = 2 a b + b c + c a } 1 V = 2 S a b a b c + b c a b c + c a a b c 1 V = 2 S 1 c + 1 a + 1 b Re-arranging the terms, 1 V = 2 S 1 a + 1 b + 1 c . Hence proved that, 1 V = 2 S 1 a + 1 b + 1 c .

E M B I B E

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>REVIEW EXERCISES>Q 10

HARD

8th CBSE

IMPORTANT

Earn 100

A hollow garden roller which is $49 cm$ wide and has a girth of $176 cm$ is made of $2 cm$ thick cast iron. Find the volume of iron and weight of roller if $1 {cm}^{3}$ of iron weighs $7.5$ grams.

Important Questions on Mensuration-II (Solid Figures)

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>THINKING SKILLS>Q 1

A wall

15 m

long,

30 cm

wide and

4 m

high is made of bricks, each measuring

22 cm \times 12 cm \times 7.5 cm .

If

\frac{1}{12}

of the total volume of the wall consists of mortar how many bricks are there in a wall?

HARD

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>THINKING SKILLS>Q 2

The area of adjaecent faces of a cuboid are

x, y

and

z

. Show that the volume of a the cuboid is

\sqrt{x y z}

.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>THINKING SKILLS>Q 3

If

V

is the volume of a cuboid of dimensions

a \times b \times c

and

S

is its surface area, then prove that

\frac{1}{V} = \frac{2}{S} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})

.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>THINKING SKILLS>Q 4

A circular wire of radius

42 cm

is cut and bent in the form of a rectangle whose sides are in the ratio of

6 : 5

. Find the smaller side of the rectangle.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>VALUES AND LIFE SKILLS>Q 1

If the rainfall on a particular day was

6 cm

, how many litres of water fell on a field of

2

hectares on that day? How can rainwater be harvested?

HARD

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>SOME NCERT TEXTBOOK QUESTIONS>Q 1

A suitcase with measures

80 cm \times 48 cm \times 24 cm

is to be converted with a trapaulin cloth. How many metres of trapaulin of width

96 cm

is required to cover

100

such suitcases?

EASY

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>SOME NCERT TEXTBOOK QUESTIONS>Q 2

The lateral surface area of a hollow cylinder is 4,224 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.

EASY

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>SOME NCERT TEXTBOOK QUESTIONS>Q 3

Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
To find how much it can hold.