Volume and Surface Areas Quiz Set 004

Question 1

The ratio of surface area to the volume of a cuboids is 9 : 1, and the sum of reciprocals of two edges is 62, what is the reciprocal of the third edge?

A

22 .

B

24 .

C

20 .

D

26 .

Soln.
Ans: a

The well-known relation for a cuboids is \$1/V = 2/S(1/a + 1/b + 1/c)\$, which can be re-arranged to get \$1/c = 1/2(S/V) - (1/a + 1/b)\$ = \$1/2(62) - 9\$ = 22.

Question 2

How much water flows per hour through a pipe of radius 42 cm, if water flows at 10 km/h? Take π = 22/7.

A

5544 cu. m.

B

5546 cu. m.

C

5542 cu. m.

D

5548 cu. m.

Soln.
Ans: a

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is \${22 × 42 × 42 × 10 × 1000}/{7 × 100 × 100}\$, which can easily be cancelled to get 5544 cu. m.

Question 3

What is the volume of a right cone whose cross-section is an isosceles triangle with base 18 cm and height 40 cm?

A

1080 π sq. cm.

B

1081 π sq. cm.

C

1079 π sq. cm.

D

361 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 9 cm, and height h = 40 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(9^2 × 40)\$ = 1080π.

Question 4

The ratio of surface area to the volume of a cuboids is 7 : 1, and the sum of reciprocals of two edges is 44, what is the reciprocal of the third edge?

A

15 .

B

17 .

C

13 .

D

19 .

Soln.
Ans: a

The well-known relation for a cuboids is \$1/V = 2/S(1/a + 1/b + 1/c)\$, which can be re-arranged to get \$1/c = 1/2(S/V) - (1/a + 1/b)\$ = \$1/2(44) - 7\$ = 15.

Question 5

The slant height of a right conical tent of height 5 m is 13 m. What is the curved surface area?

A

156 π sq. m.

B

157 π sq. m.

C

155 π sq. m.

D

158 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = \$√{13^2 - 5^2}\$ = \$√{169 - 25}\$ = 12. The volume is π × r × l = π × 12 × 13 = 156π sq. m. 