A solid cuboid ABCDEFGH with a rectangular base, AC = 13 cm, BC = 5cm and CH = 15cm.
(a) determine the length of AB,
AB =sqt(13^2 - 5^2)
= 12 cm
(b) Calculate the surface area of the cuboid.
SA = 2(12*5+ 12*15 +5*15)
= 2(60+180 +75)
= 2(315)
= 630 square centimeters
(c) Given that the density of the material used to make the cuboid is 7.6g/cm^3
, calculate its mass in kilograms.
= (630 *7.6)/1000
=4.788 kg
(d) Determine the number of the such cuboid that can fit exactly in a container measuring 1.5m by 1.2m by 1m.
(d) the cuboid is 15x12x5cm
The container is 1500x1200x1000 cm
so, what do you think?
12*5*15
= 900
150*120*100
=1800000
= 1800000/900
= 2000
Hmmm. You seem to have lost some zeroes.
The container's dimensions (in cuboids) are 100x100x200 = 2,000,000
To determine the number of cuboids that can fit exactly in the container, you need to calculate the volume of the cuboid and the volume of the container. Then, divide the volume of the container by the volume of the cuboid to find the number of cuboids that can fit.
Volume of the cuboid:
The volume of a rectangular solid (cuboid) is calculated by multiplying its length, width, and height. In this case, the length (AB) is 12 cm, the width (BC) is 5 cm, and the height (CH) is 15 cm. Therefore, the volume of the cuboid is:
Volume = AB * BC * CH
Volume = 12 cm * 5 cm * 15 cm
Volume = 900 cm^3
Volume of the container:
The volume of the container is given as 1.5 m by 1.2 m by 1 m. However, the units for the volume of the cuboid are in cm^3, so we need to convert the measurements to cm.
1.5 m = 150 cm
1.2 m = 120 cm
1 m = 100 cm
Therefore, the volume of the container is:
Volume = length * width * height
Volume = 150 cm * 120 cm * 100 cm
Volume = 1,800,000 cm^3
Now, you can determine the number of cuboids that can fit in the container by dividing the volume of the container by the volume of the cuboid:
Number of Cuboids = Volume of Container / Volume of Cuboid
Number of Cuboids = 1,800,000 cm^3 / 900 cm^3
Number of Cuboids = 2000
So, there would be 2000 of such cuboids that can fit exactly in the container measuring 1.5m by 1.2m by 1m