Search by Topic

Resources tagged with Surface and surface area similar to Weekly Problem 1 - 2010:

Filter by: Content type:
Stage:
Challenge level:

There are 19 results

Broad Topics > Measures and Mensuration > Surface and surface area

Take Ten

Stage: 3 Challenge Level:

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

Changing Areas, Changing Volumes

Stage: 4 Challenge Level:

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Qqq..cubed

Stage: 4 Challenge Level:

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

Painted Cube

Stage: 3 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Inside Out

Stage: 4 Challenge Level:

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Tin Tight

Stage: 4 Challenge Level:

What's the most efficient proportion for a 1 litre tin of paint?

Scientific Measurement

Stage: 4 Challenge Level:

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level:

A follow-up activity to Tiles in the Garden.

All Tied Up

Stage: 4 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

Funnel

Stage: 4 Challenge Level:

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

The Spider and the Fly

Stage: 4 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Covering Cups

Stage: 3 Challenge Level:

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

When the Angles of a Triangle Don't Add up to 180 Degrees

Stage: 4 and 5

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .

F'arc'tion

Stage: 3 Challenge Level:

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Biology Measurement Challenge

Stage: 4 Challenge Level:

Analyse these beautiful biological images and attempt to rank them in size order.

Cola Can

Stage: 4 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Plutarch's Boxes

Stage: 3 Challenge Level:

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .