Billy is making an ice-cream sundae.

From the cuboid we can see that there are 5 squares in one row on the front face . And there are two rows. So the number of squares on the front face will be 5*2 = 10 .

We know the area of square as ,

$\qquad\boxed{\sf Area_{(square)}= side^2}$

Hence the area of 10 squares will be 10x² , where x is the side length of each square. Similarly there are 10 squares at the back . Hence their area will be 10x² .

Also there are in total 12 squares sideways 6 on each sides . So their surface area will be 12x² . Hence the total surface area in terms of side of square will be ,

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies\boxed{\sf TSA_{(cuboid)}= 32x^2}$

Now let's find out the TSA in terms of side . So here the lenght of the cuboid is equal to the sum of one of the sides of 5 squares .

$\sf\implies 5x = l \\\\\sf\implies x = \dfrac{l}{5} \\\\\qquad\qquad\underline\red{ \sf Similarly \ breadth }\\\\\sf\implies b = 3x \\\\\sf\implies x = \dfrac{ b}{3}$

$\rule{200}2$

Hence the TSA of cuboid in terms of lenght and breadth is :-

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies TSA_{(cuboid)}= 20\bigg(\dfrac{l}{5}\bigg)^2+12\bigg(\dfrac{b}{3}\bigg) \\\\\sf\implies TSA_{(cuboid)}= 20\times\dfrac{l^2}{25}+12\times \dfrac{b^2}{9}\\\\\sf\implies \boxed{\red{\sf TSA_{(cuboid)}= \dfrac{4}{5}l^2 +\dfrac{4}{3}b^2 }}$

6 0

3 years ago

Please help I am really struggling:(

Nastasia [14]

The equation would be 4(-22)-5

7 0

3 years ago

Read 2 more answers

What is the true solution to 3 In 2+In 8 = 2 In(4x)?<br> 60f<br> Š O OOO<br> TNT 00

alina1380 [7]

Answer:

x = 2

Step-by-step explanation:

Taking antilogs, you have ...

2³ × 8 = (4x)²

64 = 16x²

x = √(64/16) = √4

x = 2 . . . . . . . . (the negative square root is not a solution)

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You can also work more directly with the logs, if you like.

3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2

3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents

6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify

2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)

ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2

2 = x . . . . . . . . . . . . . . . . . . . take the antilogs

4 0

3 years ago