Mensuration: Cubes, Cuboids, and a Spherical Toy Block Quiz — 5 Free Questions

📖 Read the passage, then answer the questions below

A toy manufacturer produces wooden building blocks in three shapes for a new playset. The cubical block has a side length of 6 centimetres. The cuboidal block measures 8 centimetres in length, 6 centimetres in width, and 4 centimetres in height. The spherical block, a solid ball, has a radius of 7 centimetres. Throughout this passage, use pi = 22/7.

The manufacturer packs one of each of these three blocks into a rectangular playset box measuring 40 centimetres in length, 30 centimetres in width, and 20 centimetres in height, and wants to know how efficiently the box's volume can be used compared to the space the blocks themselves occupy.

Separately, the manufacturer is also considering doubling the side length of the cubical block for a "jumbo" edition of the playset, and wants to compare the jumbo block's volume and surface area to those of the original cubical block before finalising the new design.

Question 1

What is the total surface area of the cubical block?

Question 2

What is the volume of the cuboidal block?

Question 3

If the cube's side length is doubled, what would the new surface area be?

Question 4

What is the ratio of the cube's surface area to the cuboid's surface area?

Question 5

What is the width of the playset box?

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About Mensuration: Cubes, Cuboids, and a Spherical Toy Block

CLAT's Quantitative Techniques section pairs a short data-rich scenario with several straightforward numeric questions -- here, mensuration applied to a single invented toy manufacturer's building blocks, so every answer can be worked out from the figures given, without any outside knowledge.

This quiz is built around three wooden blocks -- a cube, a cuboid, and a sphere -- plus the rectangular box they are packed into, with every dimension given up front. Every question below is answered using those same figures -- nothing new is introduced question to question.

The twenty-four questions move through the kind of angles CLAT actually tests: volume and surface area of each shape, a "jumbo edition" scaling scenario, ratios between shapes, packing calculations, and a multi-statement combination question.

Only five of the twenty-four questions are shown on any single attempt, so replaying this quiz brings a genuinely different mix of angles on the same three blocks rather than the same five memorised by rote.