Examples with solutions for Surface Area of a Cuboid: Using variables

Exercise #1

A cuboid has a surface area of 102.

Calculate X.

XXX777333

Video Solution

Answer

3

Exercise #2

Calculate X given that the surface area of the cuboid is 98.

49X

Video Solution

Answer

1

Exercise #3

The surface area of the cuboid is 18X + 7.

Calculate X.

555444XXX

Video Solution

Answer

The given surface area is not possible.

Exercise #4

Look at the cuboid in the figure below.

Its surface area 752 cm².

Calculate X.

121212888X+4X+4X+4

Video Solution

Answer

10 cm

Exercise #5

Express the surface area of the rectangular prism in terms of X using the given data.

333555XXX

Video Solution

Answer

16X+30

Exercise #6

Express the surface area of the cube in terms of a.

aaa

Video Solution

Answer

6a^2

Exercise #7

Express the surface area of the rectangular prism below in terms of a.

111555aaa

Video Solution

Answer

12a+10

Exercise #8

Express the surface area of the rectangular prism below in terms of a, b, and c.

cccaaabbb

Video Solution

Answer

2ac+2ab+2bc

Exercise #9

Look at the cuboid in the diagram.

Its surface area is 135.5.

Calculate X.

X+5X+2X+3

Video Solution

Answer

1.5

Exercise #10

The surface area of the cuboid in the diagram is 110. Calculate X.

6X+54

Video Solution

Answer

-1.9

Exercise #11

A cuboid has the following dimensions:

4×3x×2y 4\times3x\times2y

Its surface area is:

66x+56 66x+56

What is the value of y y ?

Video Solution

Answer

3.5 3.5 cm

Exercise #12

The surface area of the cuboid in the diagram is 450x cm².

a = 7

Calculate the volume of the cuboid.

aa

Video Solution

Answer

225x49 225x -49 cm³

Exercise #13

The ratio between the height and the width of the cuboid 3:5.

The length of the cuboid l and greater than 3 of the height.

Express using l the surface area of the cuboid.

hhhwwwlll

Video Solution

Answer

5827l2 \frac{58}{27}l^2

Exercise #14

The surface area of a cuboid is 300X cm².

Its height is 5X cm.

What is its width and length?

Video Solution

Answer

Width = 5

Height = 25xx+1 \frac{25x}{x+1}

Exercise #15

The surface area of a rectangular prism is 40xy2 40xy^2 .

The length of the rectangular prism isz z .

Express the possible height and width using x,y,z x,y,z .

Video Solution

Answer

z z , 10xy2z12z 10\frac{xy^2}{z}-\frac{1}{2}z

Exercise #16

A number of bricks were stacked in the shape of a box. One brick was pulled out so that a brick-sized recess was left on its side.

Calculate the surface area of ​​the new shape.

3x5.57x21.5

Video Solution

Answer

79x + 83 cm²

Exercise #17

Renovations began at a municipal swimming pool. As part of the renovations, the pool is being resurfaced with custom-made tiles.

12xx14x \frac{1}{2}x\cdot x\cdot\frac{1}{4}x (in meters).

Dimensions of the pool: depth of 5 mts.

length 20 mts.

width 10 mts.

Express the number of tiles used using x.

Video Solution

Answer

4000x3 \frac{4000}{x^3}