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Q1. Find the surface area of cubes with edge (i) 5 cm (ii) 2.9 cm.

Solution

Surface area of cube = 6(Side)². (i) Surface area of cube with edge 5 cm = 6(5)² = 6 x 25 = 150 cm² (ii) Surface area of cube with edge 2.9 cm = 6(2.9)² = 6 x 8.41 = 50.46 cm²

Q2. If the area of a rectangle is 243 sq. m and the length is 27 m, what is the breadth of the rectangle?

Solution

Area of a rectangle is given by: Area = l x b, where l = length b = breadth Here, area is given as 243 m² and its length = 27 m Thus, Area = l x b 243 = 27 x b b = 9 Thus, breadth of the rectangle = 9 m

Q3. Raju wants to fence the garden in his house which is in the shape of a rectangle having dimensions 25 m x 18 m. Find the cost of fencing at the rate of Rs 200 per metre.

Solution

The length of the fence required is the perimeter of the rectangular garden. Given that: Length (l) = 25 m ; Breadth (b) = 18 m i.e., Perimeter = 2 x (l + b) = 2 x (25 + 18) = 2 x 43 = 86 m So, the perimeter of the garden or the length of the fence required is 86 m. Cost of fencing 1 m = Rs 200 Thus, Cost of fencing 86 m = Rs 200 x 86 = Rs 17,200

Q4. A music room in a school is 4 m long, 4 m wide and 3 m high. Find the area of its four walls and the area of its floor.

Solution

Here, L = 4 m, B = 4 m and H = 3 m Area of 4 walls and the floor = 2H(L + B) + LB = 2 x 3 x (4 + 4) + 4 x 4 = 6 x 8 + 16 = 48 + 16 = 64 m²

Q5. When the perimeter of a regular polygon is divided by 5, the length of a side is 25 m. What is the name of the polygon? What is the perimeter?

Solution

A Regular polygon is a polygon with all sides of equal length. Given that the Perimeter is divided by 5 to get the length of a side. So, it is the Pentagon since it has 5 sides. Now, Perimeter = 5 x side = 25 x 5 = 125 m Thus, the perimeter of the Pentagon is 125 m.

Q6. A rectangular tank is 3 m long, 2.5 m wide and 1.4 m deep. Calculate its capacity in liters.

Solution

Here, L = 3 m, B = 2.5 m and H = 1.4 m Volume of tank = L x B x H = 3 x 2.5 x 1.4 = 10.5 m³ Now, 1 m³ = 1000 liters Therefore, Capacity of tank = 10.5 x 1000 = 10500 liters.

Q7. Find the cost of digging a cuboidal pit 6 m long, 5 m wide and 2.5 m deep at the rate of Rs 25 per m³.

Solution

Here, L = 6 m, B = 5 m and H = 2.5 m Volume of pit = L x B x H = 6 x 5 x 2.5 = 75 m³ Cost of digging = Rs 25 per m³ Therefore, total cost = Rs 25 x 75 = Rs 1875.

Q8. Find the surface area of the four walls of a cubical room whose side is 4m. Find the cost of whitewashing the room at the rate of Rs 5 per square metre.

Solution

Side of cube = 4 m Area of 4 walls = 4(Side)² = 4(4)² = 4 x 16 = 64 m². The whitewashing is done on 4 walls and 1 roof, So the surface area of 4 walls and 1 roof = 5(Side)² = 5(4)² = 5 x 16 = 80 m² Cost of whitewashing = Rs 5 x 80 = Rs 400.

Q9. The length of a side of a hexagon is 2 inches. What is the perimeter?

Solution

A Hexagon is a polygon which has 6 equal sides. Here, the length of the side = 2 inches We find the perimeter by adding the lengths of the edges. Perimeter of the hexagon = 2 + 2 + 2 + 2 + 2 + 2                                     = 6 x 2                                     = 12 inches Thus, the perimeter of the hexagon is 12 inches.

Q10. The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes. Each of side 45 cm. How many cubes are formed?

Solution

Here, length of metal block = 2.25 m = 225 cm Breadth of metal block = 1.5 m = 150 cm Height of metal block = 27 cm Volume of metal block = 225 x 150 x 27 = 911250 cm³ Side of each cube = 45 cm Volume of each cube = 45³ = 91125 cm³ Let the number of cubes made be x So the volume of x cubes = 91125x cm³ Since the metal block is melted and recast, so its volume will not change. Therefore 91125x = 911250 This gives, x = 10 Hence, 10 such cubes are made.

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