Foundation and Higher · cones and spheres

The formula is
given. The marks
are in using it.

substitute,
then calculate

pointed shapes are —

One third

a cone is ⅓ of a cylinder

a pyramid is ⅓ of a prism

step 1 of 4

Volume of a cone

1. Write the formula, then substitute.

2. 3² = 9, and ⅓ of 9 × 8 is 24.

✓ 24π is the exact answer

V = 13πr²h

= 13 × π × 3² × 8

= 24π = 75.4 cm³

step 2 of 4

Volume of a sphere

1. Cubed, not squared: 6³ = 216.

2. 216 × 4 ÷ 3 = 288.

✓ Given the diameter? Halve it first

V = 43πr³

= 43 × π × 6³

= 288π = 905 cm³

step 3 of 4

Volume of a pyramid

1. Find the area of the base first: 36.

2. Use the vertical height, not the slope.

✓ A third of the 360 cm³ prism

V = 13 × base area × h

= 13 × 6 × 6 × 10

= 120 cm³

step 4 of 4

Surface area: sphere

1. Squared this time: it is an area.

2. 4 × 36 = 144.

✓ Area in cm², volume in cm³

A = 4πr²

= 4 × π × 6²

= 144π = 452 cm²

cones, spheres, pyramids —

Substitute

into the formula you are given

Radius

not diameter: halve it

Units

cm² for area, cm³ for volume

“In terms of π”?
Stop at 24π.

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