Volume and Surface Areas Quiz Set 003 | Maths Aptitude Quiz Questions and Mock Test on Volume and Surface Areas Set 3 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

The slant height of a right conical tent of height 21 m is 29 m. What is the curved surface area?

580 π sq. m.

581 π sq. m.

579 π sq. m.

582 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = $√{29^2 - 21^2}$ = $√{841 - 441}$ = 20. The volume is π × r × l = π × 20 × 29 = 580π sq. m.

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Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 6 cm and height 4 cm?

12 π sq. cm.

13 π sq. cm.

11 π sq. cm.

5 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 3 cm, and height h = 4 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(3^2 × 4)$ = 12π.

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Question 3

What is the volume of a cone generated by rotating a right angled triangle with sides 29, 21 and 20 cm? The rotation is done about the side of length 20 cm.

2940 π sq. cm.

2941 π sq. cm.

2939 π sq. cm.

981 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 21 cm, and height h = 20 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(21^2 × 20)$ = 2940π.

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Question 4

How much water flows per hour through a pipe of radius 17 cm, if water flows at 10 km/h?

289 π cu. m.

291 π cu. m.

287 π cu. m.

293 π 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 π × ${17 × 17 × 10 × 1000}/{100 × 100}$, which can easily be cancelled to get 289π cu. m.

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Question 5

What is the surface area of the cuboid obtained by joining two equal cubes of 64 cu. cm volume each?

160 sq. cm.

162 sq. cm.

158 sq. cm.

164 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L³ = 64, which gives L = 4. The resulting cuboid has L = L, H = L, and B = 2L. The surface area is 2 × (LB + BH + HL) = 2 × (2L² + 2L² + L²) = 10 × L² = 10 × 4² = 160 sq. cm.

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