All categories

3 years ago

The triangular prism has a volume of 27 cubic units.

Mathematics

2 answers:

Neporo4naja [7]3 years ago

7 0

Answer:

1 cubic unit will be the volume of the prism.

Step-by-step explanation:

Volume of the triangular prism = 27 cubic units

Since formula of volume of the triangular prism = (1/3)A×h

27 = (1/3)A×h ⇒ Ah = 27×3 = 81

Now each side of the prism is dilated then we have to calculate the volume of new prism.

V' = (1/3)×A'×h'

= (1/3) (1/9)A×(1/3)h = (1/81)×Ah = (1/81)×81 = 1 cubic unit

Therefore the volume of new prism will be 1 cubic unit

Scrat [10]3 years ago

3 0

Answer:

1 cubic unit

Step-by-step explanation:

We are given that

Volume of triangular prism $V_1$ = 27 cubic units

We are given that each side of triangular prism dilated by a factor of 1/3.

We have to find the new volume of triangular prism.

We have a relationship between the volumes

$V_2=k^3V_1$

Where $k=$ scale factor

$V_2$ = Volume of triangular prism after applying the scale factor on each side

$V_1$ =Original volume of triangular prism

Substitute the values then we get

$V_2=(\frac{1}{3})^3(27)==1$ cubic unit

Answer: 1 cubic unit

You might be interested in

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?

zysi [14]

Given Information :-

⠀

Each exterior angle of a regular polygon has a measure of 40°

⠀

To Find :-

⠀

The number of sides of the polygon

⠀

Formula Used :-

⠀

$\qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star$

⠀

Solution :-

⠀

Using the formula,

⠀

$\sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star$

⠀

Thus, the polygon is a nonagon, and hence has 9 sides.

⠀

$\underline{\rule{227pt}{2pt}} \\ \\$

5 0

2 years ago

Find the straight-time pay: $9.25 per hour, 35 hours.

beks73 [17]

Answer:

you will get paid $323.75 if you work 35 hours and get paid $9.25 per hour

6 0

2 years ago

Read 2 more answers

Simplify. Rewrite the expression in the form 5”. (5-8)(5-1) =

chubhunter [2.5K]

Answer:

$(5 ^{ - 8} )( {5}^{ - 10} ) = {5}^{ - 18} = 2.62 \times {10}^{ - 13}$

I hope I helped you^_^

5 0

3 years ago

Read 2 more answers

PLS HELP ASAP I WILL GIVE BRAINERLIST PLUS 10 POINTS

Tresset [83]

It’s the 3rd answer choice

6 0

3 years ago

2 points

natima [27]

Answer:

4.9 feet

Step-by-step explanation:

First, we need to determine the height of the building using the following:

$L^2 = H^2 + B^2$

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

$20^2 = H^2 + 10^2$

$400 = H^2 + 100$

$H^2 = 400 - 100$

$H^2 = 300$

$H = \sqrt{300$

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

$L_2^2 = H^2 + B_2^2$

Where

$L_2 = 18$ --- Length of the second ladder

$H = \sqrt{300$ ----- Height of the building

So, we have:

$18^2 = \sqrt{300}^2 + B_2^2$

$324 = 300 + B_2^2$

$B^2_2 = 324 - 300$

$B^2_2 = 24$

Solving for B2, we have:

$B_2 = \sqrt{24$

$B_2 = 4.9$

8 0

3 years ago