A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high -Maths 9th

1 Answer

Answer :

From the question statement, we have Edge of a cube = 10cm Length, l = 12.5 cm Breadth, b = 10cm Height, h = 8 cm (i) Find the lateral surface area for both the figures Lateral surface area of cubical box = 4 (edge)2 = 4(10)2 = 400 cm2 …(1) Lateral surface area of cuboidal box = 2[lh+bh] = [2(12.5×8+10×8)] = (2×180) = 360 Therefore, Lateral surface area of cuboidal box is 360 cm2. …(2) From (1) and (2), lateral surface area of the cubical box is more than the lateral surface area of the cuboidal box. The difference between both the lateral surfaces is, 40 cm2. (Lateral surface area of cubical box – Lateral surface area of cuboidal box=400cm2–360cm2 = 40 cm2) (ii) Find the total surface area for both the figures The total surface area of the cubical box = 6(edge)2 = 6(10 cm)2 = 600 cm2…(3) Total surface area of cuboidal box = 2[lh+bh+lb] = [2(12.5×8+10×8+12.5×100)] = 610 This implies, Total surface area of cuboidal box is 610 cm2..(4) From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And their difference is 10cm2. Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm2

Related questions

Description : A cubical box has each edge 10 cm -Maths 9th

Last Answer : (i) Lateral surface area of cubical box = 4a2 = 4 x 102 = 400 cm2 Lateral surface area of cuboidal box = 2h (l + b) = 2 x 8(12.5 +10) = 16 X 22.5 = 360 cm2 Thus, lateral surface area of ... x 305cm2 = 610 cm2 Thus, total surface area of cuboidal box is greater by (610 - 600) cm2 = 10 cm2

Description : Hameed has built a cubical water tank with lid for his house, with each other edge 1.5m long. -Maths 9th

Last Answer : Edge of cubical tank = 1.5 m ∴ Area of 4 walls = 4 (side)² = 4(1.5)² m² = 4 x 225 = 9 m² Area of floor = (1.5)² = 2.25 m² ∴ Total surface area = 9 + 2.25 = 11.25 m² Edge of square tile = 25 m = 0.25 m² ∴ Area of 1 tile = (0.25)2 = .0625 m²

Description : A cuboidal water tank is 6m long, 5m wide and 4.5m deep. How many litres of water can it hold? -Maths 9th

Last Answer : Dimensions of a cuboidal water tank are: l = 6 m and b = 5 m and h = 4.5 m Formula to find volume of tank, V = l b h Put the values, we get V = (6 5 4.5) = 135 ... water, 135 m3volume hold = (135 1000) litres = 135000 litres Therefore, given cuboidal water tank can hold up to135000 litres of wate

Description : A matchbox measures 4 cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes? -Maths 9th

Last Answer : Dimensions of a matchbox (a cuboid) are l×b×h = 4 cm×2.5 cm×1.5 cm respectively Formula to find the volume of matchbox = l×b×h = (4×2.5×1.5) = 15 Volume of matchbox = 15 cm3 Now, volume of 12 such matchboxes = (15×12) cm3 = 180 cm3 Therefore, the volume of 12 matchboxes is 180cm3.

Description : A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm × 5 cm × 2 cm -Maths 9th

Last Answer : 92239223% Volume of cone = 1313πr2h = 13×227×1×7=22313×227×1×7=223 cu. cm Volume of cubical block = (10 × 5 × 2) cm3 = 100 cm3 ∴ Wastage of wood = (100−227)100×100(100−227)100×100 = 27832783% = 92239223%

Description : If three cubes of copper, each with an edge 6 cm, 8 cm and 10 cm respectively are melted to form a single cube, -Maths 9th

Last Answer : 20.8 cm Let the edge of the single cube be ‘a’ cm. Then, total volume melted = Volume of cube formed ⇒ (6)3 + (8)3 + (10)3 = a3 ⇒ a3 = 216 + 512 + 1000 = 1728 ... Diagonal of the new cube = 3–√a=(3–√×12)3a=(3×12) cm = 20.8 cm (approx.)

Description : A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5cm. Find the outer curved surface of the bowl. -Maths 9th

Last Answer : Inner radius of hemispherical bowl = 5cm Thickness of the bowl = 0.25 cm Outer radius of hemispherical bowl = (5+0.25) cm = 5.25 cm Formula for outer CSA of hemispherical bowl = 2πr2, where r is radius of ... 22/7) (5.25)2 = 173.25 Therefore, the outer curved surface area of the bowl is 173.25 cm2.

Description : The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m -Maths 9th

Last Answer : Length (l) and depth (h) of tank is 2.5 m and 10 m respectively. To find: The value of breadth, say b. Formula to find the volume of a tank = l b h = (2.5 b 10) m3= 25b m3 Capacity ... of water (Given) Therefore, 25000 b = 50000 This implies, b = 2 Therefore, the breadth of the tank is 2 m.

Description : Find the cost of digging a cuboidal pit 8m long, 6m broad and 3m deep at the rate of Rs 30 per m3 -Maths 9th

Last Answer : The given pit has its length(l) as 8m, width (b)as 6m and depth (h)as 3 m. Volume of cuboidal pit = l×b×h = (8×6×3) = 144 (using formula) Required Volume is 144 m3 Now, Cost of digging per m3 volume = Rs 30 Cost of digging 144 m3 volume = Rs (144×30) = Rs 4320

Description : A cuboidal water tank is 6 m long, -Maths 9th

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Description : A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

Description : A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

Description : Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. -Maths 9th

Last Answer : Volume of rectangular box=lbh=16(64)=1024cm3 Volume of sphere=34​πr3=33.5238cm3 16 sphere=16(33.5238)=536.3808 Volume of liquid=1024−536.3808=488cm3

Description : Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. -Maths 9th

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Description : A rectangular piece of paper is 22 cm long and 10 cm wide. -Maths 9th

Last Answer : Since rectangular piece of paper of rolled along its length. ∴ 2πr = 22 r = 22 × 7 / 2 × 22 = 3.5 cm Height of cyclinder (h) = 10 cm ∴ Volume of cyclinder = πr2h = 22 / 7 × 3.5 × 3.5 × 10 = 385 cm3.

Description : A rectangular piece of paper is 22 cm long and 10 cm wide. -Maths 9th

Last Answer : Since rectangular piece of paper of rolled along its length. ∴ 2πr = 22 r = 22 × 7 / 2 × 22 = 3.5 cm Height of cyclinder (h) = 10 cm ∴ Volume of cyclinder = πr2h = 22 / 7 × 3.5 × 3.5 × 10 = 385 cm3.

Description : A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. -Maths 9th

Last Answer : Length of greenhouse, say l = 30cm Breadth of greenhouse, say b = 25 cm Height of greenhouse, say h = 25 cm (i) Total surface area of greenhouse = Area of the glass = 2[lb+lh+bh] = [2(30 ... (30+25+25)] (after substituting the values) = 320 Therefore, 320 cm tape is required for all the 12 edges.

Description : Shahid has built a cubical water tank with lid for his house, -Maths 9th

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Description : A hemispherical bowl made of brass has inner diameter 10.5cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm2. -Maths 9th

Last Answer : Inner radius of hemispherical bowl, say r = diameter/2 = (10.5)/2 cm = 5.25 cm Formula for Surface area of hemispherical bowl = 2πr2 = 2 (22/7) (5.25)2 = 173.25 Surface area of hemispherical ... of tin-plating the inner side of the hemispherical bowl at the rate of Rs 16 per 100 cm2 is Rs 27.72.

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Last Answer : Edge of cube (a) = 10 cm (i) ∴ Lateral surface area = 4a² = 4 x (10)² = 4 x 100 cm²= 400 cm² (ii) Total surface area = 6a² = 6 x(10)² cm² = 6 x 100 = 600 cm²

Description : Rinku has built a cuboidal water tank in his house. The top of the water tank is covered with an iron lid. -Maths 9th

Last Answer : Total inner surface area of the water tank including the base without top = 2(l + b) h + l b = 2(180 + 120) 60 + 180 120 = 36000 + 21600 = 57600 cm2 Area of each title = 10 ... 57600 / 80 = 720 Total amount required for 720 tiles at the rate of 480 per dozen = 480 / 12 720 = 28800

Description : Rinku has built a cuboidal water tank in his house. The top of the water tank is covered with an iron lid. -Maths 9th

Last Answer : Total inner surface area of the water tank including the base without top = 2(l + b) h + l b = 2(180 + 120) 60 + 180 120 = 36000 + 21600 = 57600 cm2 Area of each title = 10 ... 57600 / 80 = 720 Total amount required for 720 tiles at the rate of 480 per dozen = 480 / 12 720 = 28800

Description : A cement concrete road is 1000 m long, 8 m wide and 15 cm thick over the sub-base of 10 cm thick gravel. The box cutting in road crust is (A) 500 m3 (B) 1000 m3 (C) 1500 m3 (D) 2000 m3

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Description : If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. -Maths 9th

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Description : Find the area of a triangle having perimeter 32cm. One side of its side is equal to 11cm and difference of the other two is 5cm. -Maths 9th

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Description : Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid. -Maths 9th

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Description : Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid. -Maths 9th

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Description : How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm? -Maths 9th

Last Answer : ∵ Volume of one brick = (25 × 11.25 × 6) cm3 and volume of the wall = (800 × 600 × 22.5) cm3 ∴ Number of bricks = Volume of the walls / Volume of one brick = 800 × 600 × 22.5 / 25 × 11.25 × 6 = 6400

Description : How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm? -Maths 9th

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Description : The number of planks of dimensions (4 m x 50cm x 20cm) that can be stored in a pit which is 16 m long, 12 m wide and 40 m deep is -Maths 9th

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Description : The number of planks of dimensions (4 m x 50cm x 20cm) that can be stored in a pit which is 16 m long, 12 m wide and 40 m deep is -Maths 9th

Last Answer : Solution of this question

Description : 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 being 2 m wide. -Maths 9th

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Description : A cylindrical drum of 15cm radius and 70cm height is full of water. The water is emptied into a rectangular tank 225cm long and 70cm wide. Find the height of water level in the tank. a) 3.5cm b) 2.25cm c) 3.142cm d) 1.57cm

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Description : How can you work out the volume of a cube of edge 5cm?

Last Answer : 5 x 5 x 5 = 125 cubic cm

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Description : How many metres of 5 m wide cloth will be required to make a conical tent, the radius of whose base is 3.5 m and height is 12 m ? -Maths 9th

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Description : If the difference in elevation of an edge of the pavement 9 m wide and its crown is 15 cm, the camber of the pavement, is (A) 1 in 60 (B) 1 in 45 (C) 1 in 30 (D) 1 in 15

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Description : The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. -Maths 9th

Last Answer : This answer was deleted by our moderators...