Area & Volume, General Mathematics

Question: A river `1.5 m`deep and `36` m wide is flowing at the rate of `3.5` km per hour. The amount of water that runs into the sea per minute ( in cubic metres) is :
A
`3150`

B
`31500`

C
`6300`

D
`63000`

Note: Length of water column flower in `1` min. `= ((3.5 xx 100)/(60)) m` `= 175/3 m.` :. Volume flower per minute `= (175/3 xx 36 xx 3/2) cu. m` `= 3150 cu. m.`
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Question: The area of the card board needed to make a box of size `24 cm xx 12 cm xx 5 cm` will be :
A
`1440 cm^2`

B
`468 cm^2`

C
`936 cm^2`

D
720 cm^2`

Note: Area of the cardboard `= 2(24 xx 12 + 12 xx 5 + 24 xx 5) cm^2` `= 936 cm^2.`
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Question: A hall is `15` m long and `12` m broad. The sum of the areas of the floor and the ceiling is equal to the sum of areas of the areas of the four walls. The volume of the hall is :
A
`1200 m^3`

B
`1800 m^3`

C
`900 m^3`

D
`720 m^3`

Note: `2(15 + 12) xx h` `= 2(15 xx 12)` `or h = 180/27 m` `= 20/3 m.` :. Volume `= (15 xx 12 xx 20/3) m^3` `= 1200 m^3.`
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Question: An open box is made of wood `3` cm thick. Its external dimensions are `1.46 m``1.16 m` and `8.3 dm.` The cost of painting the inner surface of the box at `50` paise per `100` sq. cm is :
A
`Rs. 277`

B
`Rs. 138.50`

C
`Rs.415.50`

D
`Rs. 554`

Note: Internal length `= (146 - 6) cm = 140 cm,` Internal breadth `= (116 - 6) cm` `= 110 cm.` Internal depth `= (83 - 3) cm` `= 80 cm.` :. Area of inner surface `= [2 (1 + b) xx h] + 1b` `= [2 (140 + 110) xx 80 + 140 xx 110] sq. cm` `= 55400 sq. cm.` Cost of painting `= Rs. (1/2 xx 1/100 xx 55400)` `= Rs. 277`
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Question: The dimensions of an open box are `50` cm, `40` cm and `23 cm.` Its thickness is `3 cm.` If `1` cubic cm of metal used in the box weighs `0.5 gms,` the weight of the box is :
A
`8.56 kg`

B
`8.04 kg`

C
`7.576 kg`

D
`6.832 kg`

Note: Volume of the metal `= [(50 xx 40 xx 23) - (44 xx 34 xx 20)] cu. cm.` `= 16080 cu. cm.` Weight of the metal `= ((16080 xx 0.5)/1000) kg` `= 8.04 kg.`
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Question: How many bags of gain can be stored in a cuboid granary`12 m xx 6 m xx 5 m,` if each bag occupies a space of `0.48 cu.`metre ?
A
`75`

B
`750`

C
`480`

D
`288`

Note: Number of bags `= Volume of granary/Volume of one bag` `= ((12 xx 6 xx 5)/(0.48))` `= 750`
1. Report
Question: If the length of diagonal of a cube is `4√3 cm,` then its surface area is :
A
`24 cm^2`

B
`54 cm^2`

C
`96 cm^2`

D
`216 cm^2`

Note: Not available
1. Report
Question: If the length of diagonal of a cube is `8√3 cm,`then its volume is :
A
`512 cm^3`

B
`384 cm^3`

C
`64 cm^3`

D
`192 cm^3`

Note: `√3 a = 8√3 ⇒ a = 8 cm.` :. Volume` = (8 xx 8 xx 8) cm^3` `= 512 cm^3.`
1. Report
Question: The number of small cubes with edge `10 cm` that can be accomodated in a cubical box of `1` metre edge is :
A
`10`

B
`100`

C
`1000`

D
`10000`

Note: Number of cubes `= ((100 xx 100 xx 100)/(10 xx 10 xx 10))` `= 1000.`
1. Report
Question: A metal sheet `27` cm long, `8` cm broad and `1` cm thick is melted into a cube. The difference between surface areas of two solids, is :
A
`284 cm^2`

B
`286 cm^2`

C
`296 cm^2`

D
`300 cm^2`

Note: Not available
1. Report

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Question: A river `1.5 m`deep and `36` m wide is flowing at the rate of `3.5` km per hour. The amount of water that runs into the sea per minute ( in cubic metres) is :

Question: The area of the card board needed to make a box of size `24 cm xx 12 cm xx 5 cm` will be :

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

Question: An open box is made of wood `3` cm thick. Its external dimensions are `1.46 m``1.16 m` and `8.3 dm.` The cost of painting the inner surface of the box at `50` paise per `100` sq. cm is :

Question: The dimensions of an open box are `50` cm, `40` cm and `23 cm.` Its thickness is `3 cm.` If `1` cubic cm of metal used in the box weighs `0.5 gms,` the weight of the box is :

Question: How many bags of gain can be stored in a cuboid granary`12 m xx 6 m xx 5 m,` if each bag occupies a space of `0.48 cu.`metre ?

Question: If the length of diagonal of a cube is `4√3 cm,` then its surface area is :

Question: If the length of diagonal of a cube is `8√3 cm,`then its volume is :

Question: The number of small cubes with edge `10 cm` that can be accomodated in a cubical box of `1` metre edge is :

Question: A metal sheet `27` cm long, `8` cm broad and `1` cm thick is melted into a cube. The difference between surface areas of two solids, is :