Volume and surface area Questions and answers

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Elementary Mathematics

11). If each side of a cube is decreased by 19%, then decrease in surface area is

A). 40%

B). 38.40%

C). 35%

D). 34.39%

View Answer

Correct Answer: 34.39%

Here, x = y = -19%

According to the formula,

Percentage decrease in surface area

= \( \Large \left[ x + y + \frac{xy}{100} \right] \)%

= \( \Large \left[ -19 - 19 = \frac{ \left(-19\right) \times \left(-19\right) }{100} \right] \)%

= \( \Large \left[ -38 + \frac{361}{100} \right] \)%

= \( \Large \left[-38 + 3.61 \right] \% \) = - 34.39%

12). 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.

A). 2068 sq cm

B). 1825 sq cm

C). 1925 sq crn

D). 2160 sq cm

View Answer

Correct Answer: 2068 sq cm

Total surface area of cylinder

= \( \Large 2 \pi r \left(h + r\right) \)

Given that, \( \Large r = \frac{14}{2} \) = 7 cm, h = 40 cm

Therefore, Required total surface area

= \( \Large 2 \times \frac{22}{7} \times 7 \times \left(40 + 7\right) \)

= \( \Large 44 \times 47 = 2068 sq. cm. \)

13). If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the radius of its base. (n = 3.14)

A). 5 cm

B). 8 cm

C). 3 cm

D). 4cm

View Answer

14). A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 in length of uniform thickness. The diameter of the wire is

A). \( \Large \frac{2}{10} \) cm

B). \( \Large \frac{2}{\sqrt{10}} \) cm

C). \( \Large \frac{1}{\sqrt{10}} \) cm

D). \( \Large \frac{1}{10} \) cm

View Answer

Correct Answer: \( \Large \frac{2}{\sqrt{10}} \) cm

Given,

\( \Large r_{1} \) = 1 cm, \( \Large h_{1} \) = 30 cm, \( \Large h_{2} \) = 300 cm

Volume of rod = Volume of wire

=> \( \Large \pi r_{1}^{2}h_{1} = \pi r_{2}^{2}h_{2} \)

=> \( \Large \pi \times \left(1\right)^{2} \times 30 = \pi \times r_{2}^{2} \times 300 \)

=> \( \Large r_{2}^{2} = \frac{30}{300} \)

Therefore, \( \Large r_{2} = \frac{1}{\sqrt{10}}cm \)

Therefore, diameter = 2\( \Large r_{2} \)

\( \Large \frac{2}{\sqrt{10}} cm \)

15). What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?

A). 10 cm

B). 12 cm

C). 15 cm

D). 16 cm

View Answer

Correct Answer: 16 cm

Let the height and radius of solid cylinder be h and r cm respectively.

Given that, radius (r) = 5 cm

and total surface area = 660 \( \Large cm^{2} \)

=> \( \Large 2 \pi rh + 2 \pi r^{2} = 660 \)

=> \( \Large 2 \pi r \left(h + r\right) = 660 \)

=> \( \Large \left(h + 5\right) = \frac{330}{5 \pi } = \frac{330}{5} \times \frac{7}{22} \)

=> \( \Large h = \frac{66 \times 7}{22} -5 = 21 - 5 \)

Therefore, Required height = 16 cm

16). What will be the curved surface area of a right circular cylinder having length 160 cm and radius of the base is 7 cm?

A). 6020 sq cm

B). 5052 sq cm

C). 7045 sq cm

D). 7040 sq cm

View Answer

17). The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3. The ratio of their volumes will be

A). 4 : 9

B). 9 : 4

C). 20 : 27

D). 27 : 20

View Answer

18). If the radius of a cylinder is increased by 25% and its height remains unchanged. then find the per cent increase in volume.

A). 56.25%

B). 52.25%

C). 50.40%

D). 60.26%

View Answer

Correct Answer: 56.25%

According to the formula,

Percentage increase in volume

= \( \Large \left(2x + \frac{x^{2}}{100}\right)\% = \left(2 \times 25 + \frac{25^{2}}{100}\right)\% \)\

= \( \Large \left(50 + \frac{625}{100}\right) \)%

= 56.25%

19). A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the piller at the rate of Rs.10 per sq m.

A). Rs.50

B). Rs.68

C). Rs.98

D). Rs.55

View Answer

20). A piller 14 cm in diameter is 5 m high. How much material was used to construct it?

A). \( \Large (77 \times 10^{2}) cm^{3} \)

B). \( \Large (77 \times 10^{4}) cm^{3} \)

C). \( \Large (77 \times 10^{5}) cm^{3} \)

D). \( \Large (77 \times 10^{3}) cm^{3} \)

View Answer

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