A 12 cm by 12 cm ice cube tray is in the shape of a cuboid with twelve hemispheres inset. The depth of each hemispheres is 1 cm.
a) If all the hemispheres were filled with water, calculate the total volume of water that the ice cube tray could hold.
It is now desired to paint the top of the ice cube tray a pleasant shade of blue.
b) calculate the surface area of one hemisphere on the tray.
c) Calculate the total surface area of the top of the ice cube tray.
Thank you so much for huge help!!!!!
My answer for a) 25.1cm^3
B) 6.28. m^2
C) here I'm not sure, I don't understand question. Is it only flat too then the answer should be144 m2.
Thank you so much, please help me:))
a) To calculate the total volume of water that the ice cube tray could hold, we need to find the volume of the cuboid and the volume of each hemisphere, and then add them together.
The cuboid has dimensions of 12 cm by 12 cm by 1 cm. To find its volume, we multiply these dimensions together:
Volume of cuboid = 12 cm * 12 cm * 1 cm = 144 cm^3
Next, we need to find the volume of each hemisphere. Since there are twelve hemispheres, we multiply the volume of one hemisphere by twelve:
Volume of one hemisphere = (4/3) * π * (radius)^3
Given that the depth of each hemisphere is 1 cm, the radius of each hemisphere can be found by subtracting 1 cm from half the side length of the cube:
radius = (1/2) * (12 cm - 1 cm) = 5.5 cm
Now we can calculate the volume of one hemisphere:
Volume of one hemisphere = (4/3) * π * (5.5 cm)^3
Finally, we add the volume of the cuboid and the volume of the twelve hemispheres together to find the total volume of water that the ice cube tray could hold:
Total volume = Volume of cuboid + (Volume of one hemisphere * 12)
b) To find the surface area of one hemisphere on the tray, we need to calculate the area of the curved portion of the hemisphere. The formula for the surface area of a sphere is 4πr^2, and since we are only considering half a sphere (a hemisphere), we divide the formula by 2:
Surface area of one hemisphere = (1/2) * 4 * π * (radius)^2
c) To calculate the total surface area of the top of the ice cube tray, we need to consider both the flat surface of the cuboid and the flat surface of the twelve hemispheres. The flat surface area of the cuboid is simply the length times the width:
Surface area of cuboid = 12 cm * 12 cm
Since the tray has twelve hemispheres, and each hemisphere has a flat surface area of πr^2, the total surface area of the flat surfaces of the twelve hemispheres is:
Surface area of twelve hemispheres = 12 * π * (radius)^2
To find the total surface area of the top of the ice cube tray, we add the surface area of the cuboid to the surface area of the twelve hemispheres:
Total surface area of top = Surface area of cuboid + Surface area of twelve hemispheres
I hope this helps! Let me know if you have any further questions.
To calculate the total volume of water that the ice cube tray can hold, we first need to calculate the volume of the cuboid part and the volume of the twelve hemispheres. Then we can sum them up.
a) Volume of the cuboid part:
The ice cube tray is 12 cm by 12 cm and has a depth of 1 cm.
Volume = length × width × height = 12 cm × 12 cm × 1 cm = 144 cm³
b) Volume of each hemisphere:
Radius of the hemisphere = 12 cm / 2 = 6 cm
Volume of a hemisphere = 2/3 × π × (radius)³ = 2/3 × π × 6 cm × 6 cm × 6 cm ≈ 904.77 cm³
Since there are twelve hemispheres, the total volume of the hemispheres = 12 × 904.77 cm³ ≈ 10,857.24 cm³
To find the total volume of water that the ice cube tray can hold, we sum the volume of the cuboid and the volume of the hemispheres:
Total volume = Volume of cuboid part + Volume of hemispheres = 144 cm³ + 10,857.24 cm³ ≈ 11,001.24 cm³
Therefore, the correct answer for a) is approximately 11,001.24 cm³.
Now let's move on to the second part of the question.
b) To calculate the surface area of one hemisphere, we only need to consider the curved surface area.
The formula for the curved surface area of a hemisphere is given by:
Surface Area = 2 × π × (radius)²
Substituting the radius with 6 cm:
Surface Area = 2 × π × (6 cm)² = 2 × π × 36 cm² ≈ 226.2 cm²
Therefore, the correct answer for b) is approximately 226.2 cm².
c) To calculate the total surface area of the top of the ice cube tray, we need to consider both the flat surface area of the cuboid and the flat surface area of the twelve hemispheres.
The flat surface area of the cuboid part:
Surface Area = 2 × (length × width) = 2 × (12 cm × 12 cm) = 288 cm²
The flat surface area of each hemisphere (top part):
The radius of the hemisphere is 6 cm.
The formula for the surface area of a sphere is given by:
Surface Area = 4 × π × (radius)²
Substituting the radius with 6 cm:
Surface Area = 4 × π × (6 cm)² = 4 × π × 36 cm² ≈ 452.4 cm²
Since there are twelve hemispheres:
Total flat surface area of the hemispheres = 12 × 452.4 cm² ≈ 5,428.8 cm²
To find the total surface area of the top of the ice cube tray, we sum the surface area of the cuboid and the surface area of the hemispheres:
Total surface area = Surface area of cuboid + Total flat surface area of the hemispheres
= 288 cm² + 5,428.8 cm² ≈ 5,716.8 cm²
Therefore, the correct answer for c) is approximately 5,716.8 cm².
I hope this explanation helps! Let me know if you have any further questions.