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4 years ago

1- Find the surface area and volume of each solid figure.

Mathematics

1 answer:

Bess [88]4 years ago

7 0

Answer:

Volume

Figure 1 = 56 cube units

figure 2 = 60 cube units

figure 3 =72 cube units

Surface area

Figure 1 = 100 square units

figure 2 = 104 square units

figure 3 =108 square units

Step-by-step explanation:

From the all figure we can see that each figure made up of unit cubes

Figure 1

Surface area

Large cuboid portion =2 x (6 x 2 ) + (6 x 4) + 2 x(4 x 2) + 16

= 24 + 24 + 16 + 16 = 80 unit square

Small cuboid portion = (4 x 2) + (2 x 2) + (4 x 2) = 8 + 4 + 8 = 20

Total surface area = 80 + 20 = 100 unit square

Volume

Small cuboid = 4 x 2 = 8

Large cuboid = 6 x 4 x 2 = 48 cube unit

Total volume = 48 + 8 = 56 cubs units

Figure 2

Surface area

Total surface area =24 + 18 + 36 + 20 + 6 = 104 unit square

Volume

Small cuboid = 6 x 2 = 12

Large cuboid = 6 x 4 x 2 = 48 unit square

Total volume = 48 + 12 = 60 cube units

Figure 3

Surface area

Total surface area = 48 + 36 + 24 = 108 square units

Volume

Total volume = 6 x 4 x 3 = 72 cube units

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2/5 of 60 please help

klasskru [66]

Answer:

60/5 is equal to 12. so 12 x 2= 24, and 5 x 12=60, so 24/60, or just 24

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side.

jasenka [17]

Answer:

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x -----> the possible lengths of the third side

Applying the Inequality Theorem

1) 12+8 > x

20 > x

Rewrite

x < 20 in

2) 8+x > 12

x> 12-8

x > 4 in

therefore

4 in < x < 20 in

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

3 0

3 years ago

What percent is equivalent to

Soloha48 [4]

Answer:

20%

Step-by-step explanation:

To change a fraction to a percentage , multiply by 100%

$\frac{8}{40}$ × 100%

= 0.2 × 100%

= 20%

8 0

3 years ago

12) A candy company used 8 gallons of syrup to make 4 batches of candy. What is the rate of syrup per batch?

Black_prince [1.1K]

The answer is 2 gallons of syrup per batch.

3 0

3 years ago

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

$g(0)=1$

Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

$g(x)=f(x)+2$

$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}-2$

$g(2)=-2$

Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!

8 0

3 years ago