Formulae and Substitution: Practice Questions

Given the formula \( S = \frac{n}{2}(a + l) \), find the value of \( S \) when \( n = 10 \), \( a = 4 \) and \( l = 16 \).

If \( x = -3 \) and \( y = 4 \), calculate the value of the expression \( 2x^2 - 3y + 5 \).

Given the formula \( A = \frac{1}{2}h(a + b) \), find the value of \( A \) when \( h = 8 \), \( a = 5 \) and \( b = 7 \).

Given the formula \( F = \frac{9}{5}C + 32 \), calculate the value of \( F \) when \( C = 25 \).

Given the formula \( E = mc^2 \), find the value of \( E \) when \( m = 0.5 \) and \( c = 10 \).

Find the value of \( y \) in the formula \( y = 3x - 5 \) when \( x = -4 \).

Given the formula \( E = \frac{1}{2}mv^2 \), find the value of \( v \) if \( E = 100 \) and \( m = 8 \), assuming \( v > 0 \).

Given the formula for the volume of a cone \( V = \frac{1}{3}\pi r^2 h \), find the value of \( V \) when \( r = 3 \) and \( h = 7 \). (Take \( \pi = \frac{22}{7} \))

The formula for the total surface area \( A \) of a closed cylinder is given by \( A = 2\pi r(r + h) \), where \( r \) is the radius and \( h \) is the height.

(a) Find the value of \( A \) when \( r = 7 \) and \( h = 10 \). (Take \( \pi = \frac{22}{7} \))
(b) Make \( h \) the subject of the formula.
(c) If the total surface area is \( 440 \text{ cm}^2 \) and the radius is \( 5 \text{ cm} \), find the height \( h \) of the cylinder. (Take \( \pi = \frac{22}{7} \))