**Exercise 18.1**

**Question 1: Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.**

**Solution:**

^{2}

^{2}and Lateral Surface Area is 4800 cm

^{2}.

**Question 2: Find the lateral surface area and total surface area of a cube of edge 10 cm.**

**Solution:**

^{2}

^{2}

^{2}

^{2})

^{2}

^{2}and Lateral Surface area of cube is 400cm

^{2}.

**Question 3: Find the ratio of the total surface area and lateral surface area of a cube.**

**Solution:**

^{2}

^{2}

^{2})/(4(Side)

^{2})

**Question 4: Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with colored paper with a picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth, and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?**

**Solution:**

^{2}

^{2 }

^{2}

**Question 5: The length, breadth, and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 m**

^{2}.**Solution:**

^{2}

^{2}is Rs. 7.50

^{2}= 74 × 7.50

^{2}= Rs. 555

^{2}is Rs.555.

**Question 6: Three equal cubes are placed adjacently in a row. Find the ratio of a total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.**

**Solution:**

^{2}

^{2})

^{2}

^{2}

^{2}/18a

^{2}

**Question 7: A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.**

**Solution:**

^{3}= 4

^{3}= 64

^{3}

^{3}

^{3}/1cm

^{3}= 64

^{2}

**Question 8: The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.**

**Solution:**

**Question 9: Hameed has built a cubical water tank with lid for his house, with each other edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles if the cost of tiles is Rs. 360 per dozen.**

**Solution:**

^{2 }

^{2}

**Question 10: Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.**

**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}- 6a

^{2}

^{2 }-12a

^{2})/2

^{2}/2

^{2})/(6a

^{2})×100

^{2})/(12a

^{2})×100

**Question: 11 The dimensions of a rectangular box are in the ratio of 2: 3: 4 and the difference between the cost of covering it with a sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m**

^{2}is Rs. 1248. Find the dimensions of the box.**Solution:**

^{2}+ 12x

^{2}+ 8x

^{2})

^{2}

^{2}

^{2 }

^{2}

^{2},

^{2}× 2m

^{2 }

^{2}× 2

^{2}

^{2}- Rs. 416x

^{2}

^{2}

^{2}

^{2}

^{2}= 16

**Question 12: A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs 5 per meter sheet, a sheet being 2 m wide.**

**Solution:**

^{2}

**Question 13: Ravish wanted to make a temporary shelter for his car by making a box-like structure with the tarpaulin that covers all the four sides and the top of the car (with the front face of a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how many tarpaulins would be required to make the shelter of height 2.5m with base dimensions 4m × 3m?**

**Solution:**

^{2}

^{2}.

**Question 14: An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface of Rs. 50 per sq. metre.**

**Solution:**

^{2}

^{2}

**Question 15: The cost of preparing the walls of a room 12m long at the rate of Rs. 1.35 per square meter is Rs. 340.20 and the cost of matting the floor at 85paise per square meter is Rs. 91.80. Find the height of the room.**

**Solution:**

^{2}

^{2}

**Question 16: The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs 3.50 per square meter.**

**Solution:**

^{2}

^{2}

^{2}

^{2}

**Question 17: The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 meters. The cost of decorating its walls (including doors and windows) at Rs. 6.60 per square meter is Rs. 5082. Find the length and breadth of the room.**

**Solution:**

^{2}

**Question 18: A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85cm (See figure 18.5). The thickness of the plank is 5cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm**

^{2}. Find the total expenses required for polishing and painting the surface of the bookshelf.

**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}area = Rs. 0.20

^{2}area = 21700 * 0.20

^{2}area = Rs. 4340

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}area = Rs. 0.10

^{2}area = 19350 * 0.10

^{2}area = Rs.1935

**Question 19: The paint in a certain container is sufficient to paint on an area equal to 9.375 m**

^{2}, how many bricks of dimension 22.5cm × 10cm × 7.5cm can be painted out of this container?**Solution:**

^{2}

^{2 }

^{2}

**Exercise 18.2**

**Question 1: A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many liters of water can it hold?**

**Solution:**

**Question 2: A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?**

**Solution:**

**Question 3: Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m**

^{3}.**Solution:**

^{3}

^{3}= Rs. 30

^{3}= 144 x 30

^{3}= Rs. 4320

^{3}is Rs. 4320

**Question 4: 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)**

**Solution:**

**Question 5: The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, Prove that V**

^{2}= xyz.**Solution:**

^{2}b

^{2}c

^{2}

^{2}_______(1)

^{2}= xyz

**Question 6: If the areas of three adjacent face of a cuboid are 8cm2, 18cm2 and 25cm2. Find the volume of the cuboid.**

**Solution:**

^{2}= lb

^{2}= bh

^{2}= lh

^{2}

^{2}

^{2}= 3600

^{3}.

**Question 7: The breadth of a room is twice its height, one half of its length and the volume of the room is 512dm**

^{3}. Find its dimensions.**Solution:**

^{3}

^{3}

^{3}

**Question 8: A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?**

**Solution:**

^{3}

**Question 9: Water in a canal 30 dm wide and 12 dm deep, is flowing with a velocity of 100 km every hour. What much area will it irrigate in 30 minutes if 8 cm of standing water is desired?**

**Solution:**

^{3}

^{2}

**Question 10: Three metal cubes with edges 6cm, 8cm, 10cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.**

**Solution:**

^{3}= (6

^{3}+ 8

^{3}+ 10

^{3})

^{3}= 1728

^{3}

^{3}

^{3}

^{2}

^{2}

^{2}

^{3}, 864cm

^{2}and 12√3cm.

**Question 11: Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.**

**Solution:**

^{3}

^{3}

^{3}

^{2}

^{2}.

**Question 12: Half cubic meter of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.**

**Solution:**

^{3}= 0.5 m

^{3}

^{2}

^{3})/(2 × 10000 m

^{2})

**Question 13: A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.**

**Solution:**

^{3}

^{3}

^{3}

^{3}

^{3}

^{3}

^{3}

**Question 14: The dimensions of a cinema hall are 100 m, 50 m, 18 m. How many persons can sit in the hall, if each person requires 150m**

^{3}of air?**Solution:**

^{3}

**Question 15: Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.**

**Solution:**

**Question 16: A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of a fluid can be placed in it? Also, find the volume of the wood used in it.**

**Solution:**

^{3}

^{3}

^{3}

^{3}

^{3}.

**Question 17: The external dimensions of a closed wooden box are 48cm, 36cm, 30cm. The box is made of 1.5cm thick wood. How many bricks of size 6 cm × 3 cm × 0.75 cm can be put in this box?**

**Solution:**

^{3}

^{3}

^{3}

**Question 18: How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 gms. Find the weight of the empty box in kg.**

**Solution:**

^{3}

**Question 19: A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.**

**Solution:**

^{3 }

^{3 }

^{3}

^{2}

**Question 20: A rectangular container, whose base is a square of side 5cm, stands on a horizontal table, and holds water up to 1cm from the top. When a solid cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.**

**Solution:**

^{3}

^{3}

^{3}= 25 + 2

^{3}= 27

^{3}

^{3}and 3cm.

**Question 21: A field is 200 m long and 150 m broad. There is a plot, 50 m long and 40 m broad, near the field. The plot is dug 7m deep and the earth taken out is spread evenly on the field. By how many meters is the level of the field raised? Give the answer to the second place of decimal.**

**Solution:**

^{3}

**Question 22: A field is in the form of a rectangular length 18m and width 15m. A pit 7.5m long, 6m broad and 0.8m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.**

**Solution:**

^{2}

^{3}

**Question 23: A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes?**

**Solution:**

^{2}

^{2}and length equal to the distance travelled in 45 minutes with the speed 16 km/hour.

**Question 24: Water in a rectangular reservoir having base 80m by 60m is 6.5m deep. In what time can the water be pumped by a pipe of which the cross-section is a square of side 20 cm if the water runs through the pipe at the rate of 15km/hr.**

**Solution:**

^{3}

^{3}

**Question 25: A village having a population of 4000 requires 150liters of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?**

**Solution:**

^{3}

**Question 26: A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in Fig. 18.12. If the edge of each cube is 3cm, find the volume of the structure built by the child.**

**Solution:**

^{3}

^{3}

^{3}

^{3}

**Question 27: A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.**

**Solution:**

^{3}

_{w}) = 1.5 m

_{w}) = 1.25 m

_{w}) = 0.5 m

_{w}× b

_{w}× h

_{w }

^{3}

**Question 28 : A wall of length 10 m was to be built across an open ground. The height of the wall is 4m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required?**

**Solution:**

^{3}

**Exercise VSAQs**

**Question 1: If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.**

**Solution:**

^{3}

**Question 2: Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down into a single cube whose diagonal is 12√3cm. Find the edges of three cubes.**

**Solution:**

^{3}+ (4x)

^{3}+ (5x)

^{3}

^{3}+ 64x

^{3}+ 125x

^{3}

^{3}

^{3}

^{3}=(12)

^{3}

^{3}= (12×12×12)/216

^{3}= 8

**Question 3: If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.**

**Solution:**

^{2 }

^{2 }

^{2}

^{2}