The plan is a circle, so looking down on the solid gives a round outline. That narrows it to a solid with a circular top or base.

Both elevations are triangles, which is what you see looking at a cone from the front and from the side. A cylinder would give rectangles instead.

So the solid is a cone.

A cylinder has the same circular plan, so the plan on its own cannot tell the two apart. The elevations can.

Here the sides slope in to a point at the top, instead of standing straight up, which is what a cone looks like from the front and not what a cylinder looks like.

The plan is a circle of radius \(2\) cm, so its area is

\(\pi r^2 = \pi \times 2^2 = 4\pi\ \text{cm}^2\)

The height plays no part in the plan at all.

The front elevation is the view from the front, so it shows the width and the height of the cuboid.

The plan is \(5\) squares across and \(4\) squares up, so the width is \(5\) cubes.

The side elevation is \(4\) squares across and \(3\) squares up, so the height is \(3\) cubes. The \(4\) is the depth, which the front elevation does not show.

So the front elevation is a rectangle \(5\) squares wide and \(3\) squares tall.

The plan is a circle with a dot at its centre.

The answer is the cone: the dot marks the point of the cone, which stands above the middle of its circular base. A cylinder has a plain circle for a plan, with no dot, and a square-based pyramid and a triangular prism have a square and a rectangle for plans.

Read the height of each column off the elevations. The four columns are \(4\), \(1\), \(1\) and \(1\) cubes tall.

\(4 + 1 + 1 + 1 = 7\) cubes.

The front elevation is the view from the front, so its greatest height is the tallest column: \(4\) cm.

The plan is what you see looking straight down. Every column that has at least one cube in it fills the same square, however tall it is — so the plan shows the footprint and nothing about height.

The elevations are the views from the side, and those are what carry the heights.

The plan is the view looking straight down from above.

Looking down on a cylinder standing on its end, all you see is the circle at the top, so the plan is a circle.

The front elevation is the view from the front, and looking at a cylinder from the side gives a rectangle.

Its height is the height of the cylinder, \(12\) cm.

Its width is the full width of the cylinder, which is the diameter and not the radius:

\(2 \times 4 = 8\) cm

The plan is the view from above, so it is the face the cuboid would leave if you pressed it onto the page: \(9\) cm by \(5\) cm.

The height plays no part in the plan at all.

The front elevation is the view from the front: a rectangle \(9\) cm across and \(7\) cm tall.

\(9 \times 7 = 63\ \text{cm}^2\)

Looking from the side, the width is hidden and the depth is what you see, so this rectangle is \(5\) cm across and \(7\) cm tall.

\(5 \times 7 = 35\ \text{cm}^2\)

The front elevation is what you see looking straight at the front. Each column of the drawing is as tall as the tallest stack in that line, front or back, because a taller stack behind still shows over a shorter one in front.

Left: the taller of \(3\) and \(1\) is \(3\).

Middle: the taller of \(1\) and \(2\) is \(2\).

Right: the taller of \(2\) and \(2\) is \(2\).

So the front elevation is three columns of squares, \(3\), \(2\) and \(2\) tall.

Looking from the left-hand side, each column of the side elevation is one row of the solid. Its height is the tallest stack in that row, because a taller stack behind a shorter one still shows over it.

Front row: the tallest is \(3\).

Middle row: the tallest is \(3\).

Back row: the tallest is \(5\).

From the left-hand side the front row is on the right of the drawing and the back row is on the left.

So the side elevation is three columns of squares, \(5\), \(3\) and \(3\) tall from left to right.

The plan is what you see looking straight down on the solid. Every stack of cubes is seen from above as one square, however tall it is, and a place with no cubes is left blank.

The solid has \(5\) stacks of cubes, so the plan is \(5\) shaded squares, in \(2\) rows of the grid and \(3\) columns. The front of the solid is at the bottom of the plan, and its left-hand side is on the left.

The front elevation shows the width and the height of the cuboid, but not its depth. The volume gives the depth.

The front elevation is \(3\) cm by \(3\) cm, so its area is

\(3 \times 3 = 9\ \text{cm}^2\)

Volume is this area multiplied by the depth, so

\(\text{depth} = 45 \div 9 = 5\) cm

The side elevation shows the depth and the height, so it is a rectangle \(5\) cm across and \(3\) cm up. Shade \(5\) squares across and \(3\) squares up from the bottom left corner.