Solution Let r and R be the inner and outer radii of the hollow sphere. Given that, inner diameter d = cm; inner radius r = cm; thickness = mm = cm Outer radius R = . cm Volume of hollow sphere = p R cu. units = .
cm But, density of brass in cm = . gm Total mass = = gm Therefore, total mass is . grams. Mensuration Progress Check .
What is the ratio of volume to surface area of a sphere? . The relationship between the height and radius of the hemisphere is . .
The volume of a sphere is the product of its surface area and . . . Volume of frustum of a cone Let H and h be the height of cone and frustum respectively, L and l be the slant height of the same.
If R, r are the radii of the circular bases of the frustum, then volume of the frustum of the cone is the difference of the volumes of the two cones. V R H r H h Since the triangles ABC and ADE are similar, the ratio of their corresponding sides are proportional. Therefore, H h H = r R ⇒ H hR R … ( ) V = R H r H h H R r h hR R r R r h [using ( ) ] hR R r h Volume of a frustum = p h R Rr ) cu. units Example .
If the radii of the circular ends of a frustum which is cm high are cm and cm, find the volume of the frustum. Solution Let h, r and R be the height, top and bottom radii of the frustum. Given that, h = cm, R = cm, r = cm Volume = p R Rr h cu.