Question

geodesic dome is a structure built in an almost spherical shape—a structure made from struts set on large circles. Because of its curved walls and ceiling, these domes use approximately a third less surface area to enclose the same volume as a traditional box home.





Figure 1
If height of cylindrical part is 6 cm, and total height of the model is 13 cm, then find the radius of hemisphere.
(i) 5 cm (ii) 3 cm (iii) 7 cm (iv) 4 cm

(b) A square band of side 17 cm is put outside along the edge of the hemisphere as shown in figure 1. Find the area of metal sheet required for the band.
(i) 145 cm2 (ii) 125 cm2 (iii) 135 cm2 (iv) 155 cm2

(c) A test tube is cylindrical in shape with hemispherical base of diameter 2 cm as shown in figure 2. If it is filled with chemical solution up to the height of 7 cm, then find the volume of
chemical solution in the test tube. Figure 2
(i) π cm3 (ii) 8π cm3 (iii) π cm3 (iv) π cm3

(d) Two hemispheres of same radius are joined end to end along their base.
Find the total surface area of solid so obtained.
(i) 4r2 (ii) r2 (iii) 2r2 (iv) 6r2 ​

Answer 1

Answer:

1.c(7 cm)

2.c(135 cm^2)

3.20/3π cm^3

4.4πr^2