Question 1

The total surface area of a solid hemisphere of radius $r$ is:

Accepted Answer

The curved surface area of a hemisphere is $2\pi r^2$ and the area of the circular base is $\pi r^2$. Therefore, the total surface area is $2\pi r^2 + \pi r^2 = 3\pi r^2$.

Question 2

The formula for the volume of a cylinder of radius $r$ and height $h$ is:

Accepted Answer

The volume of a cylinder is given by the product of the base area and height, which is $\pi r^2 h$.

Question 3

If the radius of a sphere is doubled, its surface area becomes:

Accepted Answer

The surface area of a sphere of radius $r$ is $S1 = 4\pi r^2$. When radius becomes $2r$, the new surface area is $S2 = 4\pi (2r)^2 = 4\pi (4r^2) = 16\pi r^2 = 4S1$. Thus, it becomes 4 times.

Question 4

The curved surface area of a right circular cone of radius $r$ and slant height $l$ is:

Accepted Answer

The curved surface area of a cone is given by the formula $\pi r l$.

Question 5

The total surface area of a solid cylinder of radius $r$ and height $h$ is:

Accepted Answer

The total surface area of a cylinder includes the curved surface area ($2\pi r h$) and the areas of the two circular bases ($2\pi r^2$), which equals $2\pi r h + 2\pi r^2 = 2\pi r(r + h)$.

Surface Areas and Volumes