If the volume of an isosceles right-angled triangular prism is $k {\mathrm{cm}}^3$, find the value of $k$.

1. Cuboid:

If length of Cuboid is $l,$ breadth is $b$ and height is $h$ then,

(i) Total surface area of a Cuboid $=2(lb+bh+lh)$

(ii) Lateral surface area of a Cuboid $=2h(l+b)$

(iii) Volume of a Cuboid $=lbh$

2. Cube:

If the length of the edge of a Cube is $l$ units, then

(i) Total surface area of a Cube $=6l^2$

(ii) Lateral surface area of a Cube $=4l^2$

(iii) Volume of a Cube $=l^3$

3. Volume of Pyramid:

The volume of a Pyramid is $\frac{1}{3}$rd volume of a Right Prism if both have the same base and same height.

4. Right Circular Cylinder:

(i) A Cylinder is a solid having two circular ends with a curved surface area.

(ii) If the line segment joining the centres of base and top is perpendicular to the base, it is called right circular cylinder.

(iii) If the radius of Right Circular Cylinder is $r$ and height is $h$ then;

(a) Curved surface area of a cylinder $=2\pi rh$

(b) Total surface area of a cylinder $=2\pi r(r+h)$

(c) Volume of a cylinder $=\pi r^{2}h$

5. Cone:

(i) Cone is a geometrical shaped object with circle as base, having a vertex at the top.

(ii) If the line segment joining the vertex to the centre of the base is perpendicular to the base, it is called right circular cone.

(iii) The length joining the vertex to any point on the circular base of the cone is called slant height $\left(l\right)$, $l^2=h^2+r^2$

(iv) If $‘r’$ is the radius, $‘h’$ is the height, $‘l’$ is the slant height of a cone, then

(a) Curved surface area of a cone $=\pi rl$

(b) Total surface area of a cone $=\pi r(r+l)$

(v) The volume of a cone is $\frac{1}{3}$rd the volume of a cylinder of the same base and same height i.e. volume of a cone $=\frac{1}{3}\pi r^{2}h$

6. Sphere:

(i) A sphere is an geometrical object formed where the set of points are equidistant from the fixed point in the space.

(ii) The fixed point is called centre of the sphere and the fixed distance is called radius of the sphere.

(iii) If the radius of sphere is $‘r’$ then,

(a) Surface area of a sphere $=4\pi r^2$

(b) Volume of a sphere $=\frac{4}{3}\pi r^3$

7. Hemisphere:

(i) A plane through the centre of a sphere divides it into two equal parts, each of which is called a hemisphere.

(ii) Curved surface area of a hemisphere $=2\pi r^2$

(iii) Total surface area of a hemisphere $=3\pi r^2$

(iv) Volume of a hemisphere $=\frac{2}{3}\pi r^3$