A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove

A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units

PIT_PIT [3949]

Step $1$

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

$V1=\pi r^{2} h$

In this scenario

$r=8\ units \\ h=15\ units$

Insert the values

$V1=\pi 8^{2} 15$

$V1=960\pi\ units^{3}$

Step $2$

Calculate the volume of a cone

We are aware that

the volume of a cone equals

$V2=\frac{1}{3}\pi r^{2} h$

In this example

$r=8\ units \\ l=17\ units \\ h=?$

Use the Pythagorean Theorem to determine the height h

$h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units$

$V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}$

Step $3$

Calculate the empty volume inside the cylinder

$V1-V2=960\pi -320\pi =640\pi \ units^{3}$

Thus

the final result is

the empty volume inside the cylinder is $640\pi \ units^{3}$

6 0

8 days ago

Read 2 more answers

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and poin

babunello [3666]

Answer:

(a)

The distance from A to B to C equals 40 yards.

(b)

w is less than 40.

Step-by-step explanation:

The information provided states:

The distance from A to B is 15 yards.

Thus, AB is 15 yards.

The distance from B to C is 25 yards.

Therefore, BC is 25 yards.

(a)

The total distance from A to B to C is given by AB plus BC.

A to B to C = 15 + 25.

The total distance is 40 yards.

(b)

The direct distance from A to C (AC) must be shorter than the length of A to B to C.

AC is less than AB plus BC.

AC must be less than 15 + 25.

Thus, AC is less than 40 yards.

w is less than 40.

8 2

12 days ago

Read 2 more answers

El área de una propiedad en metros cuadrados, mide 704/5. Se construye una casa que ocupa 5/6 del área total. La mitad del área

tester [3938]

Answer:

The remaining area available for construction is $\frac{704}{60}\ m^{2}$

Step-by-step analysis:

The inquiry in English reads

The total area of a property, measured in square meters, amounts to 704/5. A house is constructed occupying 5/6 of this area. Half of the leftover space is utilized for a terrace; thus, how much area remains for additional construction?

We know that

The total area is represented by the fraction 6/6

A house accounts for 5/6 of the entire area

Thus, the remaining area is (6/6)-(5/6)=1/6 of the overall area

If half of this leftover area is designated for a terrace

then

the terrace occupies (1/6)/2=1/12 of the total area

consequently,

The area remaining for construction is 1/12 of the total area

therefore

$(\frac{1}{12})\frac{704}{5} =\frac{704}{60}\ m^{2}$

8 0

3 days ago

How much would it cost to buy 100 shares in ODX group Inc and 300 shares

PIT_PIT [3949]

Complete Question

The entire question can be found in the first uploaded image

Answer:

The expense for acquiring 100 shares of ODX group Inc and 300 shares of peer Comms Lts is

$C = \$ 775$

Step-by-step explanation:

From the chat, the expense for 100 shares of ODX is $\$175$

The price of 100 shares of peer Comms Lts is $\$ 200$

Thus, the cost for 300 shares of peer Comms Lts amounts to $k = 3 * 200 = \$ 600$

Overall, the total cost for 100 shares of ODX group Inc and 300 shares of peer Comms Lts can be calculated as

$C = 175 + 600$

$C = \$ 775$

7 0

18 days ago

A builder buys bricks at the rate of $4.50 per brick for the first 10, $3.50 per brick for the next 10, and $2.50 for any additi

babunello [3666]

Purchasing the first 10 bricks at $4.50 each totals $45. The subsequent 10 bricks at $3.50 each add $35. This uses $80, leaving $20 to buy bricks priced at $2.50 each, allowing for 8 more bricks. Altogether, $100 can buy 28 bricks.

8 0

16 days ago