Short Answer TypeA hemispherical dome of a building is to be white washed. The total cost of white washing of dome building is र 924 at the rate of र 3/m2. Find the
(a) radius of the hemisphere
(b) volume of air in the dome
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l)
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
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.
A village, having a population of 4000, requires 150 litres 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?
Side of the solid cube (a) = 12 cm
∴ Volume of the solid cube = a3
= (12)3 = 12 x 12 x 12 cm3 = 1728 cm
∵ It is cut into eight cubes of equal volume.
∴ Volume of a new cube
Let the side of the new cube be x cm.
Then, volume of the new cube = x3 cm3. According to the question, x3 = 216
∴ x = (216)1/3
∴ x = (6 x 6 x 6)1/3
∴ x = 6 cm
Hence, the side of the new cube will be 6 cm. Surface area of the original cube = 6a2 = 6(12)2 cm2 Surface area of the new cube
= 6x2 = 6(6)2 cm2
∴ Ratio between their surface areas
Hence, the ratio between their surface areas is 4: 1.
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