# Two hemispheres

In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?

Correct result:

S =  10.21 cm2

#### Solution:

$r=1 \ \\ r_{2}=r/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 1^2 \doteq 3.1416 \ \\ S_{2}=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 0.5^2 \doteq 0.7854 \ \\ \ \\ S_{11}=4 \pi \cdot \ r^2/2=4 \cdot \ 3.1416 \cdot \ 1^2/2 \doteq 6.2832 \ \\ S_{22}=4 \pi \cdot \ r_{2}^2/2=4 \cdot \ 3.1416 \cdot \ 0.5^2/2 \doteq 1.5708 \ \\ \ \\ S=S_{11}+S_{22}+S_{1}-S_{2}=6.2832+1.5708+3.1416-0.7854 \doteq 10.2102 \ \\ \ \\ \text{ Correctness test: } \ \\ q=S/\pi/r^2=10.2102/3.1416/1^2=\dfrac{ 13 }{ 4 }=3.25 \ \\ \ \\ S=\dfrac{ 13 }{ 4 } \cdot \ \pi \cdot \ r^2=10.21 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Observatory
Observatory dome has the shape of a hemisphere with a diameter d = 16 m. Calculate the surface.
• The observatory
The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal needs to be covered to cover it, and 15 percent must be added to the minimum amount due to joints and waste?
• Half-sphere roof
The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents?
• Concentric circles
There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
• Fit ball
What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
• Roof tiles
The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
• Triangular prism
Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.
The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
• Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Trapezium
The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
• Earth's surface
The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?