Compute the mass of the solid $Q = \left\{(x, y, z) \in \mathbb{R}^3 \ \vert \ x, y \in \left[-\frac{300}{z+5}, \frac{300}{z+5} \right] \text{ and } 0 \leq z \leq 295 \right\}$ with density $\delta(x,y,z) = 7(z+5)$ using the change of coordinates $g: \hat{Q} \to Q$ given by $g(u,v,z) = (x, y, z) = \left(\frac{5}{z+5}u, \frac{5}{z+5}v, z \right)$. If necessary, use the approximation $\log(60) \approx4$.
My work:
We can describe $\hat{Q}$ as $\hat{Q} = \left\{(u,v,z) \ \vert \ u, v \in [-60,60] \text{ and } 0 \leq z \leq 295 \right\}$. The jacobian is easily calcuated, it's $\frac{25}{(z+5)^2}$. Then we have:
$$M = \int_{0}^{295} \int_{-60}^{60} \int_{-60}^{60} \delta(x,y,z) \cdot \frac{25}{(z+5)^2} \ \mathrm{du} \ \mathrm{dv} \ \mathrm{dz} = 175 \cdot 120^2 \cdot \log(60) = 175 \cdot 120^2 \cdot4 $$
The answer the text gives, however, is $M = 25 \cdot 120^2 \cdot 4$. Is it wrong or did I mess up somewhere here? It's like they forgot the $7$ in the density function, I'm almost certain I'm right but I wanted to make sure.