Mensuration

Write true or false: (Q1 - Q10)
1. Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is

16 π r^{2}

.
2. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is

4 π r h + 4 π r^{2}

.
3. A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is

π r [\sqrt{r^{2} + h^{2}} + 3 r + 2 h]

.
4. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is

\frac{4}{3} π a^{3}

.
5.

The capacity of a cylindrical vessel with a hemispherical portion raised upward, at the bottom as shown in figure is

\frac{π r^{2}}{3} (3 h - 2 r)

.
6. he volume of the frustrum of cone is

\frac{1}{3} π (r^{2} + R^{2} - r R) h

, where h is the vertical height of the frustrum and r, R are the radii of the ends.
7. The curved surface area of a frustrum of a cone is

π l (r_{1} + r_{2})

, where

l = \sqrt{h^{2} + ({r_{1}}^{2} + {r_{2}}^{2})}

r_{1}

and

r_{2}

are the radii of the two ends of frustrum and h is vertical height.
8. An open metallic bucket is in the shape of a frustrum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to the curved surface area of frustrum of a cone + area of circular base + curved surface area of cylinder.
9. Let R and r be the external and internal radii of a hollow cylinder of height h. Then its total surface area is

2 π (R + r) (R + h - r)

.
10. A bucket is an example of a frustums of cone.

Mensuration

Gap-fill exercise