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 rusface 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!!!!!
math - Steve, Monday, April 28, 2014 at 5:17am
if the depth of each hemisphere is 1, the that is also the radius.
a) you know how to find the volume of half a sphere, right?
b) same for surface area
c) the flat area of the top of the tray is 12x12 minus the area of 12 circles with radius 1. Now add on 12 hemispheres for the total surface area.
math - Lucas, Monday, April 28, 2014 at 6:54am
Thank you so much, a) 25.1 cm^3
b) 6.28 cm ^2
c)144-75.36 =68.64
Is it correct?
Thank you so much Steve!!!!
a) To calculate the total volume of water that the ice cube tray could hold, we need to find the volume of each hemisphere and multiply it by the number of hemispheres in the tray.
The volume of a hemisphere can be calculated using the formula: V = (2/3)πr³, where V is the volume and r is the radius.
Since the depth of each hemisphere is 1 cm, that is also the radius of each hemisphere. Therefore, the volume of each hemisphere is: V = (2/3)π(1³) = (2/3)π cm³.
Since there are 12 hemispheres in the tray, the total volume of water that the ice cube tray can hold is: (2/3)π cm³ * 12 = 8π cm³ ≈ 25.12 cm³.
b) To calculate the surface area of one hemisphere on the tray, we need to use the formula: A = 2πr², where A is the surface area and r is the radius.
Since the radius of each hemisphere is 1 cm, the surface area of each hemisphere is: A = 2π(1²) = 2π cm² ≈ 6.28 cm².
c) To calculate the total surface area of the top of the ice cube tray, we need to subtract the area of the 12 circles (hemispheres) from the total area of the top of the tray.
The total area of the top of the tray is 12 cm * 12 cm = 144 cm².
The area of 12 circles with a radius of 1 cm is: A = 12 * π(1²) = 12π cm² ≈ 37.68 cm².
Therefore, the flat area of the top of the tray is: 144 cm² - 37.68 cm² = 106.32 cm².
Finally, we need to add the surface area of the 12 hemispheres. Since each hemisphere has a surface area of 6.28 cm², the total surface area of the top of the tray is: 106.32 cm² + 6.28 cm² * 12 = 106.32 cm² + 75.36 cm² = 181.68 cm².
So the total surface area of the top of the ice cube tray is approximately 181.68 cm².
To summarize:
a) The total volume of water that the ice cube tray could hold is approximately 25.12 cm³.
b) The surface area of one hemisphere on the tray is approximately 6.28 cm².
c) The total surface area of the top of the ice cube tray is approximately 181.68 cm².