Which steps could be used to solve this equation?

Classwork 12.1 surface area

s344n2d4d5 [400]

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

6 0

3 years ago

Please help me how to figure this out I’m trying to figure out the area ASAP please

Natasha2012 [34]

Answer:

$1230.88m^{2}$

Step-by-step explanation:

Shown is one-fourth of a circle. Also, according to the picture, the radius is 28 meters.

The area for a whole circle is $2\pi r^{2}$ .

Using that information, we can find the area as if the circle was whole instead of just the fourth.

$2(\pi)(28m)^2 = 2(3.14)(784m^{2} ) = 4923.52m^{2}$

Now that we know the area of the whole circle, we just have to divide it by four to find the area of the fourth of the circle.

$4923.52m^{2} / 4 = 1230.88m^{2}$

That means that the area of the shape shown is $1230.88m^{2}$ .

I hope this helps!

4 0

3 years ago

Josh went to applebee and enjoyed a delicious steak. He enjoyed his server and wanted to give an extra special tip. Usually josh

Sonbull [250]

Answer:

Josh's total bill is $ 27.825

Step-by-step explanation:

Given:

The subtotal of the Josh Bill = $21.00

Finding the usual amount Josh gave as Tip To his sever:

Usually josh tips 20% to all servers

So Tip = 20% of his subtotal

=> $20\% \times 21$

=> $\frac{20}{100} \times 21$

=> $0.2 \times 21$

=>4.2

So Josh usually tips $4.2 to his server

Finding the amount Josh gave 25% as Tip To his sever:

But now he tips 25% which is

=> 25% of 21

=> $\frac{25}{100} \times 21$

=> $0.25 \times 21$

=> 5.25

Thus the tip amount will be $5.25

So he will be giving (5.25 - 4.2) = $1.05 more than the usual tip

Finding the total bill

The total bill = subtotal+ 7.5% sales tax + 25% tip

=> 21 + 7.5 % of 21 + 25% of 21

=> $21 + \frac{75}{100} \times 21 + \frac{25}{100} \times 21$

=> $21 +0.075 \times 21 + 0.25 \times 21$

=> 21 +1.575 +5.25

=>27.825

3 0

3 years ago

Question 2 of 10 Which describes the graph of y = (x-4)2 - 1?

WITCHER [35]

$y=(x-4)^2-1:$ $y=-\frac{4}{5}$

Sure hope this helps you

y = -4/5

4 0

2 years ago

What is the probability of rolling doubles and a sum of 6

alisha [4.7K]

3/6 look at the pic to understand

4 0

3 years ago