Question 1

The curved surface area of a right circular cylinder of height 14 cm is $88 	ext{ cm}^2$. The diameter of the base of the cylinder is:

Accepted Answer

The formula for the curved surface area of a cylinder is $2 \pi r h$. Given that $h = 14 	ext{ cm}$ and curved surface area $= 88 	ext{ cm}^2$. So, $2 	imes \frac{22}{7} 	imes r 	imes 14 = 88$. Solving for $r$, we get $4 	imes 22 	imes r = 88$, which means $88r = 88$, so $r = 1 	ext{ cm}$. T

Question 2

Total surface area of a cube whose edge is $a$ is:

Accepted Answer

A cube has 6 square faces, and the area of each square face with side length $a$ is $a^2$. Therefore, the total surface area of a cube is the sum of the areas of all its 6 faces, which is $6a^2$. Hence, the correct option is $6a^2$.

Question 3

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

Accepted Answer

The total surface area of a solid hemisphere consists of the curved surface area ($2\pi r^2$) plus the area of the circular base ($\pi r^2$). Thus, Total Surface Area $= 2\pi r^2 + \pi r^2 = 3\pi r^2$. Therefore, the correct option is $3\pi r^2$.

Question 4

The volume of a sphere of radius $r$ is given by:

Accepted Answer

The volume of a sphere is a standard formula derived in calculus and geometry, which is given as $\frac{4}{3}\pi r^3$. Therefore, the correct option is $\frac{4}{3}\pi r^3$.

Question 5

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

Accepted Answer

The curved surface area of a right circular cone is given by the formula $\pi r l$, where $r$ is the radius of the base and $l$ is the slant height. Therefore, the correct option is $\pi r l$.

Surface Areas and Volumes