Center the new cooktop's manufacturer-supplied template over the acrylic countertop's original cooktop cutout. Secure the template to the countertop with masking tape, placing the masking tape on the template's straight sides. Keep the masking tape off the template's rounded corners.
Trace the template's outline with a grease pencil. A grease pencil leaves a highly visible marking on an acrylic surface.
Remove the cooktop's template from the acrylic countertop's surface.
Cover the perimeter of the acrylic countertop's template outline with masking tape, keeping the edge of the masking tape next to the grease pencil's marking. The masking tape protects the acrylic countertop's surface from scratches.
Put on safety glasses and a dust mask.
Cut the countertop's acrylic surface, using a router equipped with a carbide-tipped router blade. Start at one corner and work around the cooktop template's outline. Keep the router's blade centered on the grease pencil's marking and the router's blade guide pressed firmly against the masking tape protecting the acrylic's surface. Discard the acrylic cutout.
Cut the countertop's plywood backing with a saber saw equipped with a wood-cutting blade, using the edge of the template outline as a cutting guide. Keep the saber saw's blade guide on the masking tape covering the countertop's acrylic surface.
Remove the masking tape protecting the acrylic countertop's surface.
Slip the cooktop into the acrylic countertop's cutout. If the cooktop's lip does not rest flush on the countertop's surface, remove the cooktop and enlarge the cutout as needed with a coarse-grit sanding block. A coarse-grit sanding block removes small amounts of the countertop without chipping the acrylic's surface.