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A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the s

Pani-rosa [81]

Answer:

The internal diameter of the sphere is 6 cm.

Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is $=\frac{diameter}{2}$

$=\frac{14}{2} \ cm$

= 7 cm.

The volume of the cone is $= \frac13 \pi r^2 h$

$=(\frac1 3\times \pi \times 7^2\times 8) \ cm^3$

$=\frac{392}{3}\pi \ cm^3$

Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is $= \frac43 \pi(R^3-r^3)$

$=\frac43 \pi (5^3-r^3) \ cm^3$

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

$\frac43 \pi (5^3-r^3) =\frac{392}{3}\pi$

$\Rightarrow 4(5^3-r^3)= 392$

$\Rightarrow 5^3-r^3=\frac{392}{4}$

$\Rightarrow 5^3-r^3=98$

$\Rightarrow -r^3=98-125$

$\Rightarrow-r^3= -27$

⇒r= 3

The internal radius of the sphere is = 3 cm.

The internal diameter of the given sphere is = (2×3) cm =6 cm.

7 0

4 years ago

Which property can be justified using the ratios in triangle CAB ?

USPshnik [31]

I think you forgot to give the diagram of the triangle along with the question. I am answering the question based on my knowledge and research. "cos B = sin (90^o - B)" is the one property among the following choices given in the question that can be justified using the ratios in triangle CAB. The correct option among all the options that are given in the question is option "C".

5 0

3 years ago

Rajiv is building a bookcase a shelf on the bookcase can hold up to 95 pounds of books write an inequality to represent the situ

mihalych1998 [28]

The first thing we must do in this type of problem is first to name the variables that we are going to use to write the inequality.
We have then:
b = the weight of books on the shelf.
The inequality is:
b <= 95
answer:
An inequality to represent the situation is
b <= 95

5 0

3 years ago

7. Marie can make 12 small mango pies for every 10 mangoes. How many pie

Marysya12 [62]

Answer:

D. Marie can make 60 pies.

Step-by-step explanation:

In this problem, we know that amount of small mango pies is directly proportional to the amount of mangoes. The amount needed for preparing an amount of pies is calculated by simple rule of three:

A. Marie can make 30 pies.

$x = \frac{10\,mangoes}{12\,pies}\times 30\,pies$