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Aptitude

61). A rectangular sheet with dimension 22 m. x 10 m. is rolled into a cylinder so that the smaller side becomes the height of the cylinder. Then the volume of the cylinder is.

A). \( \Large 385\ m^{3} \)

B). \( \Large 220\ m^{3} \)

C). \( \Large 110\ m^{3} \)

D). \( \Large 486\ m^{3} \)

View Answer

Correct Answer: \( \Large 385\ m^{3} \)

The dimension of the rectangular sheet = \( \Large 22m \times 10m \)

Height of the cylinder = 10m (given)

Circumference of the base of the cylinder = 22m

\( \Large 2 \pi r = 22 \)

\( \Large r = 22 \times \frac{7}{22} \times \frac{1}{2}=\frac{7}{2}\ m. \)

Volume of the cylinder = \( \Large \pi r^{2}h \)

=\( \Large \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 10 \)

=\( \Large 11 \times 35 = 385\ m^{3} \)

62). The height of a cylinder is 21 cm. and its curved surface is \( \Large 924\ cm^{2} \). Then the radius of the base is

A). 14 cm.

B). \( \Large \frac{7}{2} \) cm.

C). 7 cm.

D). \( \Large 2\frac{1}{2} \) cm.

View Answer

63). A cinema hall is 50 m. long and 24 m. wide what should be the height of the hall to accommodate 400 person if volume of air required for one person is \( \Large 60\ m^{3} \).

A). 12 mts.

B). 16 mts.

C). 24 mts.

D). 20 mts.

View Answer

Correct Answer: 20 mts.

Volume of air required for one person = \( \Large 60\ m^{3} \)

Volume of air required for 400 person = \( \Large 400 \times 60\ m^{3} \)

Let x be the height of the Hall

\( \Large 50 \times 40 \times x = 400 \times 60 \)

\( \Large x = \frac{400 \times 60}{50 \times 24} \) = 20 mts.

Height of the hall = 20 mts.

64). The radius of base of a cone is 7 m. If the height of the cone is 24 mts. what will be the cost of painting the surface area of the cone at Re.0.2 per square metre.

A). Rs.100

B). Rs.110

C). Rs.115

D). Rs.120

View Answer

Correct Answer: Rs.110

\( \Large l = \sqrt{h^{2}+r^{2}} \)

=\( \Large \sqrt{24^{2}+7^{2}} = \sqrt{576+49} \)

=\( \Large \sqrt{625} = 25\ mts. \)

Area to be painted = Surface area of the cone

\( \Large \pi rl \)

=\( \Large \frac{22}{7} \times 7 \times 25 \)

=\( \Large 25 \times 22 = 550\ m^{2} \)

The cost of painting per sq. mts = Re.0.2

The cost of painting the surface area of the cone = \( \Large 550 \times 0.2 \) = Rs.110

65). The ratio of radius and height of a cone is 3 : 4. Its volume is \( \Large 301.44\ cm^{3} \) \( \Large \left( \pi = 3.14\right) \), then the radius of the cone is

A). 16 cm.

B). 24 cm.

C). 6 cm.

D). 12 cm.

View Answer

Correct Answer: 6 cm.

Radius : height of a cone = 3 : 4

Let the radius be 3x, height be 4x

Volume of the cone = \( \Large \frac{1}{3} \pi r^{2}h \)

\( \Large \frac{1}{3} \pi r^{2}h \)

=\( \Large \frac{1}{3} \times \pi \times 9x^{2} \times 4x \)

=\( \Large 12x^{3} \times \pi \)

=\( \Large 12x^{3} \times \pi = 301.44 \)

=\( \Large 12x^{3} = \frac{301.44}{ \pi } \)

=\( \Large \frac{301.44}{3.14} \) = 96

\( \Large x^{3}=8 => x=2 \)

Radius of the cone = \( \Large 3 \times 2 \) = 6 cm.

66). A right cylindrical vessel is filled with water. How many right cones having same diameter and height as those of right cylinder will be needed to store the water?

A). 2

B). 3

C). 4

D). 5

View Answer

67). A cylindrical piece of metal of radius 2 cms. and height 6 crns. is shaped into a cone of the same radius. The height of the cone is.

A). 18 cm.

B). 14 cm.

C). 12 cm.

D). 8 cm.

View Answer

Correct Answer: 18 cm.

The volume of the cylindrical Piece of metal = \( \Large \pi r^{2}h \)

= =\( \Large \pi \times 2 \times 2 \times 6 = 24 \pi \ cm^{3} \)

Radius of the cone = radius of the cylinder (given)

Volume of the metal cone = \( \Large \frac{1}{3} \times \pi \times 2 \times 2 \times h\ cm^{2} \)

\( \Large \frac{1}{3} \times \pi \times 4h = 24 \pi \)

4 h = 72

h = 18 cm.

Height of the cone = 18 cm.

68). Find the volume of a solid sphere whose surface area is 616 sq.cm.

A). 4361 sq.cm.

B). 1437.3 sq.cm.

C). 4360.3 sq.cm.

D). 1437.6 sq.cm.

View Answer

Correct Answer: 1437.3 sq.cm.

Surface area of a solid sphere = \( \Large 4 \pi r^{2} \)

\( \Large 4 \pi r^{2} = 616\ sq.\ cm. \) (given)

\( \Large r^{2} = \frac{616 \times 1}{4 \pi } \)

=\( \Large \frac{616 \times 7}{88}=7 \times 7 = 49 \)

\( \Large r = \sqrt{49} = 7 cm \)

Volume of the sphere = \( \Large \frac{4}{3} \pi r^{3} \)

= \( \Large \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 \)

=\( \Large \frac{88 \times 49}{3} = 1437.3\ cm^{3} \)

69). The volume of a cone is \( \Large 9 \pi cm^{3} \), find its radius.

A). 3 cm.

B). 6 cm.

C). 2 cm.

D). 4 cm.

View Answer

70). The circular area of a solid hemisphere is 154 sq. cm.,then find the total surface area of the solid hemisphere.

A). \( \Large 462\ m^{2} \)

B). \( \Large 460\ m^{2} \)

C). \( \Large 308\ m^{2} \)

D). None of these

View Answer

Correct Answer: \( \Large 462\ m^{2} \)

Circular area = \( \Large \pi r^{2} = 154\ cm^{2} \)

\( \Large r^{2} = 154 \times \frac{7}{22}=49 \)

\( \Large r = \sqrt{49} \) = 7 cm.

Total surface area of the solid hemisphere = \( \Large 3 \pi r^{2} \)

= \( \Large 3 \times \frac{22}{7} \times 7 \times 7 = 3 \times 154 = 462\ cm^{2} \)

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