Question 1

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

Accepted Answer

4 : 21

Question 2

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

Accepted Answer

Area to be plastered= [2(l + b) x h] + (l x b) = [2(25 + 12) x 6] + (25 x 12) = (444 + 300) = 744 Cost of plastering = Rs. 744 x (75/100)= Rs. 558

Question 3

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

Accepted Answer

4 : 21

Question 4

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

Accepted Answer

Let the edge = a cm So increase by 50 % = a + a/2 = 3a/2 Total surface Area of original cube = 6 a 2 TSA of new cube = 6 3 a 2 2 = 6 9 a 2 4 = 13 . 5 a 2 Increase in area = 13 . 5 a 2 - 6 a 2 = 7 . 5 a 2 7 . 5 a 2 Increase % = 7 . 5 a 2 6 a 2 × 100 = 125%

Question 5

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

Accepted Answer

number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216

Question 6

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

Accepted Answer

12 pi cub.cm

Question 7

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

Accepted Answer

Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm. Volume of this cube = (3 x 3 x 3) cu.cm = 27 cu.cm Number of cubes = 1080 27 = 40.

Question 8

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

Accepted Answer

1200

Question 9

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

Accepted Answer

Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m 2 = 49 m 2

Question 10

How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m

Accepted Answer

No. of bricks= volume of the wall/volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400

Question 11

How many cubes of 10cm edge can be put in a cubical box of 1m edge

Accepted Answer

Number of cubes= (100x100x100) / (10x10x10)= 1000

Question 12

The surface area of a cube is 1734 sq. cm. Find its volume

Accepted Answer

Let the edge of the cube bea. Then, 6 a 2 = 1734 => a = 17 cm. Volume = a 3 = 17 3 = 4193 cu.cm

Question 13

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

Accepted Answer

Let the breadth of the wall be x metres. Then, Height = 5x metres and Length = 40x metres. x * 5x * 40x = 12.8 => x 3 = 12 . 8 / 200 = 128 / 2000 = 64 / 1000 => x = 4/10 m => x = (4/10)*100 = 40 cm

Question 14

The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:

Accepted Answer

l 2 + b 2 = d i a g o n a l 2 =40 Also, lb=20 l + b 2 = l 2 + b 2 + 2 l b = 41 + 40 =81 (l + b) = 9. Perimeter = 2(l + b) = 18 cm.

Question 15

The diagonal of a cube is 63 cm. Find its surface area

Accepted Answer

Let the edge of the cube be a. so, the diagonal a 3 = 6 3 => a=6 Surface area = 6 a 2 = 6 x 6 x 6 = 216 sq.cm

Question 16

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

Accepted Answer

Volume of new cube = 1 3 + 6 3 + 8 3 c m 3 = 729 c m 3 Edge of new cube = 729 3 = 9cm Surface area of the new cube = ( 6 x 9 x 9) sq.cm = 486 sq.cm

Question 17

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

Accepted Answer

Volume of the metal used in the box = External Volume - Internal Volume = [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm = 16080 cu.cm Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

Question 18

A town has a population of 4000 requires 140 liters of water per head. It has a tank measuring 18m x 12m x 8m. The water of this tank will suffice for ____ days?

Accepted Answer

Water required = 4000 x 140 = 560000 lit = 560 cu.m (1 cu.m = 1000 lit) Volume of tank = 18 x 12 x 8 = 1728 cu.m Water of this tank will suffice for = 1728/560 = 3 days.

Question 19

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:

Accepted Answer

Total volume of water displaced =(4 x 50) cu.m = 200 cu.m Rise in water level = 200 40 × 20 =0.25m = 25cm

Question 20

The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?

Accepted Answer

Side of smallest cube = L.C.M of 5, 10, 20 = 20cm Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm Number of blocks = (8000/1000) = 8

Volume and Surface Area Questions