a cuboid with length 13cm width 4cm and height h
State in terms of h the shaded face of the cuboid.
write an expression in terms of h for the volume of the cuboid.
if the volume of the cuboid is 286cm cube calculate the height h of the cuboid.
H is height (a shorter way for saying height
ok but could you give me an example of what state in terms of h means
Oh, we got ourselves a math problem with a shady cuboid. Let's solve it and shed some light on it!
The shaded face of the cuboid is the face opposite to the base. Since the base has dimensions of 13cm by 4cm, the shaded face would also have a length of 13cm and a width of 4cm. So we can say the shaded face has an area of 13cm * 4cm = 52cm².
Now, let's express the volume of the cuboid in terms of h. The volume of a cuboid is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, we know the length is 13cm, the width is 4cm, and the height is h. So the expression for the volume is V = 13cm * 4cm * h = 52h cm³.
Finally, if we are told that the volume of the cuboid is 286cm³, we can set up the equation 52h = 286 and solve for h. Dividing both sides of the equation by 52, we find h = 286cm³ / 52 = 5.5cm.
So, the height of the cuboid is h = 5.5cm. And now we've illuminated the solution!
To determine the shaded face of the cuboid, we need to understand its different faces. A cuboid has six faces: a top and bottom face, front and back faces, and two side faces. The shaded face is the face that is not specified in the question. Since the length and width are given as 13 cm and 4 cm, respectively, the shaded face will be the one on the side.
To express the shaded face in terms of h, we need to rely on the fact that a cuboid has parallel opposite faces. The length of the shaded face will be 13 cm, as it is the same as the specified length of the cuboid.
Therefore, in terms of h, the shaded face of the cuboid is 13h cm².
To find the expression for the volume of the cuboid, we use the formula: Volume = Length × Width × Height. In this case, the length is 13 cm, the width is 4 cm, and the height is h cm.
The expression for the volume of the cuboid in terms of h is: Volume = 13 × 4 × h = 52h cm³.
Now we can move on to calculating the height (h) of the cuboid when the volume is given as 286 cm³.
To find the height, we need to rearrange the formula for volume: h = Volume / (Length × Width).
Plugging in the values, we get: h = 286 cm³ / (13 cm × 4 cm) = 286 cm³ / 52 cm².
Dividing the numerator and denominator by 2, we have: h = 143 cm³ / 26 cm².
Simplifying further, we find: h ≈ 5.5 cm (rounded to one decimal place).
Therefore, the height of the cuboid is approximately 5.5 cm.
v = 13*4*h
no idea which face is shaded -- no picture available
286=52h
h = 5.5