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 5

MEDIUM

8th CBSE

IMPORTANT

Earn 100

A rectangular sheet of dimensions $33 cm \times 24 cm$ is rolled into a cylinder so that the smaller side becomes the height of the cylinder. Find the volume of the cylinder so formed.

Important Questions on Mensuration-II (Solid Figures)

HARD

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>REVIEW EXERCISES>Q 6

Two right circular cylinders of equal volumes have their height in the ratio

4 : 9

. Find the ratio of their curved surface areas.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>REVIEW EXERCISES>Q 7

Two right circular cylinders of equal heights have their radii in the ratio

2 : 5

. Find the ratio of their curved surface area and the ratio of their volumes.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>REVIEW EXERCISES>Q 8

A metal sheet

27 cm

long,

8 cm

broad and

1 cm

thick is melted into a cube. Find the difference between the surface areas of the two solids.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 18 - Mensuration-II (Solid Figures)>REVIEW EXERCISES>Q 9

A solid cubical block of fine wood costs

₹ 256

at

₹ 500 per m^{2}

. Find the length of each side and its volume.

HARD

8th CBSE

IMPORTANT

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

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.