6.5.1 Volume of Three Dimensional Shapes, PT3 Practice - Mathematics

6.5.1 Volume of Three Dimensional Shapes, PT3 Practice

Question 1:

The diagram below shows a cone with diameter 14 cm and height 6 cm.

Find the volume of the cone, in cm³.

Solution:

\begin{array}{l} Volume of a cone \\ = \frac{1}{3} π r^{2} h \\ = \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 62 \\ = 308 {cm}^{3} \end{array}

$\begin{array}{l} Volume of a cone \\ = \frac{1}{3} π r^{2} h \\ = \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 62 \\ = 308 {cm}^{3} \end{array}$

Question 2:

In the pyramid shown, the base is a rectangle.

If the volume is 20 cm², find the height of the pyramid, in cm.

Solution:

\begin{array}{l} Volume of a pyramid = \frac{1}{3} \times base area \times h \\ \frac{1}{3} \times base area \times h = 20 \\ \frac{1}{3} \times 5 \times 4 \times h = 20 \\ \frac{20}{3} \times h = 20 \\ h = 20 \times \frac{3}{20} \\ h = 3 cm \end{array}

$\begin{array}{l} Volume of a pyramid = \frac{1}{3} \times base area \times h \\ \frac{1}{3} \times base area \times h = 20 \\ \frac{1}{3} \times 5 \times 4 \times h = 20 \\ \frac{20}{3} \times h = 20 \\ h = 20 \times \frac{3}{20} \\ h = 3 cm \end{array}$

Question 3:

Diagram below shows a composite solid consisting of a right circular cone, a right circular cylinder and a hemisphere.

The volume of the cylinder is 1650 cm³. Calculate the height, in cm, of the cone.

[Use π = \frac{22}{7}]

$[Use π = \frac{22}{7}]$

Solution:

\begin{array}{l} Volume of a cylinder = π r^{2} h \\ \frac{22}{7} \times r^{2} \times 21 = 1650 \\ r^{2} = \frac{1650 \times 7}{22 \times 21} \\ = 25 \\ r = 5 c m \\ Thus the height of the cone \\ = 39 - 5 - 21 \\ = 13 c m \end{array}

$\begin{array}{l} Volume of a cylinder = π r^{2} h \\ \frac{22}{7} \times r^{2} \times 21 = 1650 \\ r^{2} = \frac{1650 \times 7}{22 \times 21} \\ = 25 \\ r = 5 c m \\ Thus the height of the cone \\ = 39 - 5 - 21 \\ = 13 c m \end{array}$

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