SURFACE AREAS AND VOLUMES - True/False

The total surface area of a cube of edge \(a\) is \(6a^{2}\).

The volume of a cube of edge \(a\) is \(6a^{3}\).

The volume of a cuboid of length \(l\), breadth \(b\) and height \(h\) is \(lbh\).

The total surface area of a cuboid is \(2(lb+bh+hl)\).

The curved surface area of a right circular cylinder of radius \(r\) and height hhh is \(2\pi rh\).

The total surface area of a right circular cylinder is \(2\pi rh\) only.

The volume of a right circular cylinder of radius \(r\) and height \(h\) is \(\pi r^{2}h\).

The curved surface area of a right circular cone is \(\pi rl\), where \(l\) is the slant height.

The total surface area of a right circular cone is \(\pi rl\) only.

The volume of a right circular cone of radius \(r\) and height \(h\) is \(\frac{1}{2}\pi r^{2}h\).

The total surface area of a sphere of radius \(r\) is \(4\pi r^{2}\).

The volume of a sphere of radius \(r\) is \(\frac{4}{3}\pi r^{3}\).

The volume of a hemisphere of radius \(r\) is \(\frac{2}{3}\pi r^{3}\).

The curved surface area of a hemisphere of radius \(r\) is \(2\pi r^{2}\).

The total surface area of a closed hemisphere (including its circular base) of radius \(r\) is \(3\pi r^{2}\).

When a solid is melted and recast into another shape without loss of material, its total volume remains unchanged.

If a solid sphere is melted and formed into a cylinder, the volume of the sphere must equal the volume of the cylinder (ignoring wastage).

Surface area is measured in cubic units and volume in square units.

If the radius of a sphere is doubled, its volume becomes four times the original volume.

If the height of a cylinder is tripled while keeping the radius same, its volume is also tripled.

For a right circular cone, the slant height is always less than the vertical height.

For any solid, if every linear dimension is scaled by a factor kkk, then its surface area is multiplied by \(k^{2}\).

For any solid, if every linear dimension is scaled by a factor kkk, then its volume is multiplied by \(k^{3}\).

The capacity of a container (like a tank or bottle) is numerically equal to its surface area.

In real-life questions about painting walls or wrapping objects, the relevant measure is usually surface area, not volume.