All categories

2 years ago

Surface area - multi step

Mathematics

1 answer:

forsale [732]2 years ago

4 0

Answer:

£208

Step-by-step explanation:

Given:

Height of solid box (h) = 20 cm

Width (w) = 80 cm

Length (l) = 10 cm

Cost of paint = £0.04 per cm²

Required:

Cost of painting the box

Solution:

✔️First, find the surface area of the box

Surface area = 2(l*w + l*h + w*h)

S.A = 2(10*80 + 10*20 + 80*20)

S.A = 2(800 + 200 + 1,600)

S.A = 2(2,600)

S.A = 5,200 cm²

✔️Find the cost of painting 5,200 cm² surface area of the box.

Cost of pianting 1 cm² = £0.04

Cost of painting 5,200 cm² = 5,200 × 0.04

Cost of painting the box = £208

You might be interested in

Look at the triangle below which of the following represents two of the angle measures of the triangle

Gelneren [198K]

Answer:

C. 60° and 80°

Step-by-step explanation:

Sum of triangle = 180°

Therefore,

8x + 4 + 6x - 2 + 10x + 10 = 180

Add like terms

8x + 6x + 10x + 4 - 2 + 10 = 180

24x + 12 = 180

24x = 180 - 12

24x = 168

x = 168/24

x = 7

Find each measure of the angles by substitute x = 7 into each expression

8x + 4 = 8(7) + 4 = 60°

6x - 2 = 6(7) - 2 = 40°

10x + 10 = 10(7) + 10 = 80°

The answer is 60° and 80°

6 0

3 years ago

Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1/2 times its abscissa.

rosijanka [135]

Answer:

(2, 3)

Step-by-step explanation:

2x + 5y = 19

5y = -2x + 19

y = $-\frac{2}{5} x + \frac{19}{5}$

P(abscissa, ordinate)

P(x, 1.5x)

P(2, 3)

$3 = -\frac{2}{5} (2) + \frac{19}{5}$

$3 = -\frac{4}{5} + \frac{19}{5}$

3 = 15/5

3 = 3

8 0

3 years ago

A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

Simplify<br> olo<br> leaving your answer in index form.

Yuliya22 [10]

Answer:

i would have helped but i the question isnt there......

Step-by-step explanation:

8 0

3 years ago

Here is the question

artcher [175]

3.17 is the answer and u can’t round to the nearest 10 cause it’s not necessary

5 0

3 years ago