Correct Answers: | |

Wrong Answers: | |

Unattempted: |

### Question 1

What is the surface area of the cuboid obtained by joining two equal cubes of 216 cu. cm volume each?

**A**

360 sq. cm.

**B**

362 sq. cm.

**C**

358 sq. cm.

**D**

364 sq. cm.

**Soln.**

**Ans: a**

Let the side of a cube be L. Then L^{3} = 216, which gives L = 6. The resulting cuboid has L = L, H = L, and B = 2L. The surface area is 2 × (LB + BH + HL) = 2 × (2L^{2} + 2L^{2} + L^{2}) = 10 × L^{2} = 10 × 6^{2} = 360 sq. cm.

### Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 24 cm and __slant height__ 20 cm?

**A**

768 π sq. cm.

**B**

769 π sq. cm.

**C**

767 π sq. cm.

**D**

257 π sq. cm.

**Soln.**

**Ans: a**

One of the right triangles of the isosceles triangle has its base = 24/2 = 12. By Pythagorean theorem, the height = $√{20^2 - 12^2}$ = $√{400 - 144}$ = 16. The radius of the base of the cone r = 12 cm, and height h = 16 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(12^2 × 16)$ = 768π.

### Question 3

A cone of height 2 cm and radius of base 4 cm is made up of modeling clay. A child reshapes it in the form of a sphere. What is the radius of the sphere?

### Question 4

What is the radius of a sphere if the ratio of volume to the surface area is 23 : 19?

### Question 5

What is the volume of a right cone whose cross-section is an isosceles triangle with base 18 cm and __slant height__ 41 cm?

**A**

1080 π sq. cm.

**B**

1081 π sq. cm.

**C**

1079 π sq. cm.

**D**

361 π sq. cm.

**Soln.**

**Ans: a**

One of the right triangles of the isosceles triangle has its base = 18/2 = 9. By Pythagorean theorem, the height = $√{41^2 - 9^2}$ = $√{1681 - 81}$ = 40. 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.

This Blog Post/Article "Volume and Surface Areas Quiz Set 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.