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!!!!!
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.
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
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 twelve hemispheres.
The volume of the cuboid can be calculated using the formula V = l × w × h, where l is the length, w is the width, and h is the height. In this case, the length and width are both 12 cm, and the height is 1 cm. So the volume of the cuboid is 12 cm × 12 cm × 1 cm = 144 cm³.
The volume of each hemisphere can be calculated using the formula V = (4/3) × π × r³, where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the hemisphere. In this case, the radius is 6 cm (half of the length of the cuboid). So the volume of each hemisphere is (4/3) × 3.14159 × 6 cm × 6 cm × 6 cm = 904.778 cm³.
Since there are twelve hemispheres, the total volume of water that the ice cube tray could hold is 144 cm³ + (12 × 904.778 cm³) = 10857.336 cm³.
b) To calculate the surface area of one hemisphere, we need to find the area of the curved surface.
The formula to calculate the surface area of a sphere is A = 4 × π × r², where A is the surface area and r is the radius of the sphere. In this case, the radius is 6 cm. So the surface area of one hemisphere is 4 × 3.14159 × 6 cm × 6 cm = 452.389 cm².
c) The top of the ice cube tray consists of the 12 × 1 cm depth of the hemispheres. So the total surface area of the top of the ice cube tray is 144 cm² + (12 × 452.389 cm²) = 5862.668 cm².
So, the total volume of water that the ice cube tray could hold is 10857.336 cm³, the surface area of one hemisphere is 452.389 cm², and the total surface area of the top of the ice cube tray is 5862.668 cm².