Surface Area and Volume of Composite Shapes

Q. A cube of side $16\text{cm}$ is given. How many cubes of side $4\text{cm}$ each will fit in the given cube?

1. $16$
2. $4$
3. $64$
4. $254$

Q. Jackson got a capsule shaped object. The dimensions of this object are represented as follows:


What will be the surface area of this object?

1. $32\pi {\text{cm}}^2$
2. $40\pi {\text{cm}}^2$
3. $48\pi {\text{cm}}^2$
4. $36\pi {\text{cm}}^2$

Q. What will be the volume of the following figure?

1. $\frac{40}{3}\pi {\text{mm}}^3$
2. $24\pi {\text{mm}}^3$
3. $\frac{32}{3}\pi {\text{mm}}^3$
4. $40\pi {\text{mm}}^3$

Q. The given figure shows two conical tanks and one cylindrical tank. $(\text{Volume}{)}_{\text{Cone A}}=(\text{Volume}{)}_{\text{Cone B}}=(\text{Volume}{)}_{\text{Cylinder}}=54\pi \text{cubic feet}$

$(\text{Radius}{)}_{\text{Cone A}}=(\text{Radius}{)}_{\text{Cylinder}}$

$(\text{Height}{)}_{\text{Cone B}}=(\text{Height}{)}_{\text{Cylinder}}$

If the radius $R$ and height $H$ are natural numbers, then what is the value of $h$ and$r?$

1. $r=3\sqrt{3}\text{ft},h=18\text{ft}$
2. $r=2\text{ft},h=12\text{ft}$
3. $r=2\sqrt{3}\text{ft},h=12\text{ft}$
4. $r=3\text{ft}h=18\text{ft}$

Q. Find the volume of the follwing figure.

1. $28\pi {\text{cm}}^3$
2. $24\pi {\text{cm}}^3$
3. $36\pi {\text{cm}}^3$
4. $12\pi {\text{cm}}^3$

Q.

A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of the altitude of the cone to the radius of its base is:

1. $\frac{1}{1}$

2. $\frac{1}{2}$

3. $\frac{2}{1}$

4. $\frac{2}{3}$