Volume and Surface Area of Solid Figures
- The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find the total surface area of the cylinder. ?
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Total surface area of cylinder = 2πr(h + r)
Given that, r = 14/2 = 7 cm, h = 40 cmCorrect Option: A
Total surface area of cylinder = 2πr(h + r)
Given that, r = 14/2 = 7 cm, h = 40 cm
∴ Required total surface area = 2 x (22/7) x 7 x (40 + 7)
= 44 x 47 = 2068 sq cm
- Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm. ?
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Given, r = 7 cm, h = 80 cm
Volume = πr2h = (22/7) x 7 x 7 x 80Correct Option: C
Given, r = 7 cm, h = 80 cm
Volume = πr2h = (22/7) x 7 x 7 x 80
= 12320 cm3
- If the side of a cube is increased by 12%, by how much per cent does its volume increase ?
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Here, k = 12%
According to the formula,
Percentage increase in volume = [(1 + k/100)3 - 1] x 100%Correct Option: A
Here, k = 12%
According to the formula,
Percentage increase in volume = [(1 + k/100)3 - 1] x 100%
= [(1 + 12/100)3 - 1] x 100%
= [(1.12)3 - 1] x 100%
= 0.404928 x 100% = 40.4928%
- If each side of a cube is decreased by 19%, then decrease in surface area is ?
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Here, x = y = -19%
According to the formula,
Percentage decrease in surface area
= [x + y + xy/100]%Correct Option: D
Here, x = y = -19%
According to the formula,
Percentage decrease in surface area
= [x + y + xy/100]%
= [- 19 - 19 + (-19) x (-19) /100]%
=[-38 + 361/100]%
= [-38 + 3.61]% = -34.39 %
- The paint in certain container is sufficient to paint an area equal to dimensions 22.5 cm x 10 cm x 7.5 cm can be painted out of this container ?
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Surface area of 1 brick
= 2 (lb + bh + lh)
= 2(22.5 x 10 + 10 x 7.5 + 7.5 x 22.5)
= 2(225 + 75 + 168.75)
= 2 x 468.75 = 937.50 cm2
= 93750/(100 x 100) = 0.09375 sq m
∴ Number of bricks = Total area/Surface area of 1 brickCorrect Option: A
Surface area of 1 brick
= 2 (lb + bh + lh)
= 2(22.5 x 10 + 10 x 7.5 + 7.5 x 22.5)
= 2(225 + 75 + 168.75)
= 2 x 468.75 = 937.50 cm2
= 93750/(100 x 100) = 0.09375 sq m
∴ Number of bricks = Total area/Surface area of 1 brick
= 9.375 / 0.09375 = 100