All categories

3 years ago

Classwork 12.1 surface area

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

6 0

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

You might be interested in

A certain 5-digit combination lock can be reset with a new combination. The lock uses numbers from 1 to 6. After a friend accide

daser333 [38]

The probability is (1/6)^5 power. Since the locks are independent of each other, you can multiply the probabilities together. There are 6 possible numbers for each lock and there are 5 locks. So the probability is (1/6)^5 power.

5 0

3 years ago

Money is borrowed at 14% simple interest. After one year, $1249.44 pays off the loan. How much was originally borrowed? I got $1

WITCHER [35]

The formula is
A=p (1+rt)
A future value 1249.22
P present value ?
R interest rate 0.14
T time 1 year
We need to solve for p
P=A÷(1+rt)
P=1,249.22÷(1+0.14×1)
P=1,095.81 round your answer
P=1096

Hope it helps

8 0

3 years ago

Which statements are true regarding the area of circle

Pavlova-9 [17]

Question:

Which statements are true regarding the area of circle D? Select two options.

The area of the circle depends on the square of the radius.

The area of circle D is 36Pi centimeters squared.

The area of circle D is 324Pi centimetres squared

The area of the circle depends on the square of pi.

The area of the circle depends on the central angle.

Answer:

The following statements are true regarding the area of circle D:

The area of the circle depends on the square of the radius
The area of circle D is 324Pi centimeters

Step-By-Step Explanation:

As we know, the formula for area of the circle is given by,

$A=\pi r^{2}$

Where, r = radius of the circle. In figure, CD = radius = 18 cm

So, the circle area can be measured as

$A=\pi(18)^{2}=324 \pi \mathrm{cm}^{2}$

From this, concluding that the circle area depends on radius square and its value is $324 \pi \mathrm{cm}^{2}$ . Hence, the statement given in option A and C are correct (reveals that option B is incorrect).

As the Pi is constant, the circle radius cannot depend on Pi value and Option D also incorrect. The area of sector of circle only depends on ratio of central angle to entire circle (So option E also incorrect).

6 0

2 years ago

Read 2 more answers

A river drops 12 ft vertically over a horizontal distance of 1500 ft.

elixir [45]

Answer:

Slope = rise / run

= -12 / 1500 (It's -12 and not 12 because a drop means it's decreasing)

= -0.008

4 0

3 years ago

Jack has 120 songs on his music player. Some are rock, some are jazz, and the rest of classical pieces. If his music player is o

muminat

2/5 and 1/3 have a common denominator of 15. 6/15, 5/15, and 4/15 add up to 15/15. So the chances of rock are 4/15. 120 divided by 15 is 8. Six times eight equals fourty eight, five times eight equals forty, and four times eight equals thirty two. So there are 48 classical songs, 40 jazz songs, and 32 rock songs.

4 0

3 years ago