Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere?

A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Correct Answer:

A) 2 cm

Description for Correct answer:

Given that, the height and radius of a right circular metal cone (solid) are 8 cm and 2 cm, respectively.

i.e., h = 8 cm and r = 2cm

Let the radius of the sphere is R.

Then, by condition,

\( \Large \frac{1}{3} \pi r^{2}h = \frac{4}{3} \pi R^{3} \)

=> \( \Large 4 \times 8 = 4 R^{3} \)

=> \( \Large R^{3} = \left(2\right)^{3} \)

=> R = 2

Therefore, Radius of the sphere = 2 cm

Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area

Comments

Similar Questions

1). Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. Let C and S denote the volume of cone and volume of sphere respectively, then which one of the following is correct?

A). C = 2S

B). S = 2C

C). C = S

D). C = 3S

2). 10 circular plates each of thickness 3 cm, each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed?

A). 264 \( \Large \pi cm^{3} \)

B). 252 \( \Large \pi cm^{3} \)

C). 236 \( \Large \pi cm^{3} \)

D). None of these

3). A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then volume of the empty space in the box is

A). \( \Large \frac{2500}{3} \pi cm^{3} \)

B). \( \Large 5000 \pi cm^{3} \)

C). \( \Large 2500 \pi cm^{3} \)

D). \( \Large \frac{5000}{3} \pi cm^{3} \)

4). What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m?

A). \( \Large \frac{1}{9} \)

B). \( \Large \frac{2}{9} \)

C). \( \Large \frac{7}{9} \)

D). \( \Large \frac{8}{9} \)

5). The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per sq m is Rs.15000, then find the height of the hall.

A). 8 m

B). 6 m

C). 9 m

D). 7 m

6). A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between

A). 370 \( \Large cm^{3} \) and 380 \( \Large cm^{3} \)

B). 380 \( \Large cm^{3} \) and 390 \( \Large cm^{3} \)

C). 390 \( \Large cm^{3} \) and 400 \( \Large cm^{3} \)

D). None of the above

7). If every interior angle of regular octagon is \( \Large 135 ^{\circ} \), then find the external angle of it.

A). \( \Large 65 ^{\circ} \)

B). \( \Large 75 ^{\circ} \)

C). \( \Large 45 ^{\circ} \)

D). \( \Large 55 ^{\circ} \)

8). In a \( \Large \triangle ABC, \angle A : \angle B : \angle C = 2 : 4 : 3 \). The shortest side and the longest side of the triangles are respectively.

A). AC and AB

B). AC and BC

C). BC and AC

D). AB and AC

9). In a \( \Large \triangle \)ABC, \( \Large \angle A = 90 ^{\circ} \), \( \Large \angle C = 55 ^{\circ} \) and \( \Large \overline{AD}\perp\overline{BC} \), What is the value of \( \Large \angle BAD \)?

A). \( \Large 60 ^{\circ} \)

B). \( \Large 45 ^{\circ} \)

C). \( \Large 55 ^{\circ} \)

D). \( \Large 35 ^{\circ} \)

10). O is the circumcentre of the \( \Large \triangle \) ABC. If \( \Large \angle BAC \) = \( \Large 50 ^{\circ} \), then \( \Large \angle OBC \) is equal to

A). \( \Large 30 ^{\circ} \)

B). \( \Large 60 ^{\circ} \)

C). \( \Large 40 ^{\circ} \)

D). \( \Large 50 ^{\circ} \)